(7y(x) − 3x + 3)y′(x) + 3y(x) − 7x + 7 = 0

4.10.47 $(7 y(x)-3 x+3) y'(x)+3 y(x)-7 x+7=0$

ODE
\[ (7 y(x)-3 x+3) y'(x)+3 y(x)-7 x+7=0 \] ODE Classiﬁcation

[[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

Book solution method
Equation linear in the variables, $y'(x)=f\left ( \frac {X_1}{X_2} \right ) $

Mathematica ✓
cpu = 1.71951 (sec), leaf count = 7785

\[\left \{\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,1\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,2\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,3\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,4\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,5\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,6\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,7\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,8\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,9\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,10\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,11\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,12\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,13\right ]}\right \},\left \{y(x)\to \frac {3 (x-1)}{7}-\frac {1}{7 \text {Root}\left [\left (2560000000000 x^{14}-35840000000000 x^{13}+232960000000000 x^{12}-931840000000000 x^{11}+2562560000000000 x^{10}-5125120000000000 x^9+7687680000000000 x^8-8785920000000000 x^7+7687680000000000 x^6-5125120000000000 x^5+2562560000000000 x^4-931840000000000 x^3+232960000000000 x^2-35840000000000 x+2560000000000 e^{\frac {140 c_1}{9}}+2560000000000\right ) \text {$\#$1}^{14}+\left (-448000000000 x^{12}+5376000000000 x^{11}-29568000000000 x^{10}+98560000000000 x^9-221760000000000 x^8+354816000000000 x^7-413952000000000 x^6+354816000000000 x^5-221760000000000 x^4+98560000000000 x^3-29568000000000 x^2+5376000000000 x-448000000000\right ) \text {$\#$1}^{12}+\left (44800000000 x^{11}-492800000000 x^{10}+2464000000000 x^9-7392000000000 x^8+14784000000000 x^7-20697600000000 x^6+20697600000000 x^5-14784000000000 x^4+7392000000000 x^3-2464000000000 x^2+492800000000 x-44800000000\right ) \text {$\#$1}^{11}+\left (28560000000 x^{10}-285600000000 x^9+1285200000000 x^8-3427200000000 x^7+5997600000000 x^6-7197120000000 x^5+5997600000000 x^4-3427200000000 x^3+1285200000000 x^2-285600000000 x+28560000000\right ) \text {$\#$1}^{10}+\left (-5891200000 x^9+53020800000 x^8-212083200000 x^7+494860800000 x^6-742291200000 x^5+742291200000 x^4-494860800000 x^3+212083200000 x^2-53020800000 x+5891200000\right ) \text {$\#$1}^9+\left (-453600000 x^8+3628800000 x^7-12700800000 x^6+25401600000 x^5-31752000000 x^4+25401600000 x^3-12700800000 x^2+3628800000 x-453600000\right ) \text {$\#$1}^8+\left (247680000 x^7-1733760000 x^6+5201280000 x^5-8668800000 x^4+8668800000 x^3-5201280000 x^2+1733760000 x-247680000\right ) \text {$\#$1}^7+\left (-21168000 x^6+127008000 x^5-317520000 x^4+423360000 x^3-317520000 x^2+127008000 x-21168000\right ) \text {$\#$1}^6+\left (-1993600 x^5+9968000 x^4-19936000 x^3+19936000 x^2-9968000 x+1993600\right ) \text {$\#$1}^5+\left (586656 x^4-2346624 x^3+3519936 x^2-2346624 x+586656\right ) \text {$\#$1}^4+\left (-57344 x^3+172032 x^2-172032 x+57344\right ) \text {$\#$1}^3+\left (2996 x^2-5992 x+2996\right ) \text {$\#$1}^2+(84-84 x) \text {$\#$1}+1\& ,14\right ]}\right \}\right \}\]

Maple ✓
cpu = 0.337 (sec), leaf count = 2417

\[\text {Expression too large to display}\] Mathematica raw input

DSolve[7 - 7*x + 3*y[x] + (3 - 3*x + 7*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (3*(-1 + x))/7 - 1/(7*Root[1 + (84 - 84*x)*#1 + (2996 - 5992*x + 2996*
x^2)*#1^2 + (57344 - 172032*x + 172032*x^2 - 57344*x^3)*#1^3 + (586656 - 2346624
*x + 3519936*x^2 - 2346624*x^3 + 586656*x^4)*#1^4 + (1993600 - 9968000*x + 19936
000*x^2 - 19936000*x^3 + 9968000*x^4 - 1993600*x^5)*#1^5 + (-21168000 + 12700800
0*x - 317520000*x^2 + 423360000*x^3 - 317520000*x^4 + 127008000*x^5 - 21168000*x
^6)*#1^6 + (-247680000 + 1733760000*x - 5201280000*x^2 + 8668800000*x^3 - 866880
0000*x^4 + 5201280000*x^5 - 1733760000*x^6 + 247680000*x^7)*#1^7 + (-453600000 +
3628800000*x - 12700800000*x^2 + 25401600000*x^3 - 31752000000*x^4 + 2540160000
0*x^5 - 12700800000*x^6 + 3628800000*x^7 - 453600000*x^8)*#1^8 + (5891200000 - 5
3020800000*x + 212083200000*x^2 - 494860800000*x^3 + 742291200000*x^4 - 74229120
0000*x^5 + 494860800000*x^6 - 212083200000*x^7 + 53020800000*x^8 - 5891200000*x^
9)*#1^9 + (28560000000 - 285600000000*x + 1285200000000*x^2 - 3427200000000*x^3
+ 5997600000000*x^4 - 7197120000000*x^5 + 5997600000000*x^6 - 3427200000000*x^7
+ 1285200000000*x^8 - 285600000000*x^9 + 28560000000*x^10)*#1^10 + (-44800000000
+ 492800000000*x - 2464000000000*x^2 + 7392000000000*x^3 - 14784000000000*x^4 +
20697600000000*x^5 - 20697600000000*x^6 + 14784000000000*x^7 - 7392000000000*x^
8 + 2464000000000*x^9 - 492800000000*x^10 + 44800000000*x^11)*#1^11 + (-44800000
0000 + 5376000000000*x - 29568000000000*x^2 + 98560000000000*x^3 - 2217600000000
00*x^4 + 354816000000000*x^5 - 413952000000000*x^6 + 354816000000000*x^7 - 22176
0000000000*x^8 + 98560000000000*x^9 - 29568000000000*x^10 + 5376000000000*x^11 -
448000000000*x^12)*#1^12 + (2560000000000 + 2560000000000*E^((140*C[1])/9) - 35
840000000000*x + 232960000000000*x^2 - 931840000000000*x^3 + 2562560000000000*x^
4 - 5125120000000000*x^5 + 7687680000000000*x^6 - 8785920000000000*x^7 + 7687680
000000000*x^8 - 5125120000000000*x^9 + 2562560000000000*x^10 - 931840000000000*x
^11 + 232960000000000*x^12 - 35840000000000*x^13 + 2560000000000*x^14)*#1^14 & ,
1])}, {y[x] -> (3*(-1 + x))/7 - 1/(7*Root[1 + (84 - 84*x)*#1 + (2996 - 5992*x +
2996*x^2)*#1^2 + (57344 - 172032*x + 172032*x^2 - 57344*x^3)*#1^3 + (586656 - 2
346624*x + 3519936*x^2 - 2346624*x^3 + 586656*x^4)*#1^4 + (1993600 - 9968000*x +
19936000*x^2 - 19936000*x^3 + 9968000*x^4 - 1993600*x^5)*#1^5 + (-21168000 + 12
7008000*x - 317520000*x^2 + 423360000*x^3 - 317520000*x^4 + 127008000*x^5 - 2116
8000*x^6)*#1^6 + (-247680000 + 1733760000*x - 5201280000*x^2 + 8668800000*x^3 -
8668800000*x^4 + 5201280000*x^5 - 1733760000*x^6 + 247680000*x^7)*#1^7 + (-45360
0000 + 3628800000*x - 12700800000*x^2 + 25401600000*x^3 - 31752000000*x^4 + 2540
1600000*x^5 - 12700800000*x^6 + 3628800000*x^7 - 453600000*x^8)*#1^8 + (58912000
00 - 53020800000*x + 212083200000*x^2 - 494860800000*x^3 + 742291200000*x^4 - 74
2291200000*x^5 + 494860800000*x^6 - 212083200000*x^7 + 53020800000*x^8 - 5891200
000*x^9)*#1^9 + (28560000000 - 285600000000*x + 1285200000000*x^2 - 342720000000
0*x^3 + 5997600000000*x^4 - 7197120000000*x^5 + 5997600000000*x^6 - 342720000000
0*x^7 + 1285200000000*x^8 - 285600000000*x^9 + 28560000000*x^10)*#1^10 + (-44800
000000 + 492800000000*x - 2464000000000*x^2 + 7392000000000*x^3 - 14784000000000
*x^4 + 20697600000000*x^5 - 20697600000000*x^6 + 14784000000000*x^7 - 7392000000
000*x^8 + 2464000000000*x^9 - 492800000000*x^10 + 44800000000*x^11)*#1^11 + (-44
8000000000 + 5376000000000*x - 29568000000000*x^2 + 98560000000000*x^3 - 2217600
00000000*x^4 + 354816000000000*x^5 - 413952000000000*x^6 + 354816000000000*x^7 -
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- 35840000000000*x^13 + 2560000000000*x^14)*#1^14 & , 10])}, {y[x] -> (3*(-1 +
x))/7 - 1/(7*Root[1 + (84 - 84*x)*#1 + (2996 - 5992*x + 2996*x^2)*#1^2 + (57344
- 172032*x + 172032*x^2 - 57344*x^3)*#1^3 + (586656 - 2346624*x + 3519936*x^2 -
2346624*x^3 + 586656*x^4)*#1^4 + (1993600 - 9968000*x + 19936000*x^2 - 19936000*
x^3 + 9968000*x^4 - 1993600*x^5)*#1^5 + (-21168000 + 127008000*x - 317520000*x^2
+ 423360000*x^3 - 317520000*x^4 + 127008000*x^5 - 21168000*x^6)*#1^6 + (-247680
000 + 1733760000*x - 5201280000*x^2 + 8668800000*x^3 - 8668800000*x^4 + 52012800
00*x^5 - 1733760000*x^6 + 247680000*x^7)*#1^7 + (-453600000 + 3628800000*x - 127
00800000*x^2 + 25401600000*x^3 - 31752000000*x^4 + 25401600000*x^5 - 12700800000
*x^6 + 3628800000*x^7 - 453600000*x^8)*#1^8 + (5891200000 - 53020800000*x + 2120
83200000*x^2 - 494860800000*x^3 + 742291200000*x^4 - 742291200000*x^5 + 49486080
0000*x^6 - 212083200000*x^7 + 53020800000*x^8 - 5891200000*x^9)*#1^9 + (28560000
000 - 285600000000*x + 1285200000000*x^2 - 3427200000000*x^3 + 5997600000000*x^4
- 7197120000000*x^5 + 5997600000000*x^6 - 3427200000000*x^7 + 1285200000000*x^8
- 285600000000*x^9 + 28560000000*x^10)*#1^10 + (-44800000000 + 492800000000*x -
2464000000000*x^2 + 7392000000000*x^3 - 14784000000000*x^4 + 20697600000000*x^5
- 20697600000000*x^6 + 14784000000000*x^7 - 7392000000000*x^8 + 2464000000000*x
^9 - 492800000000*x^10 + 44800000000*x^11)*#1^11 + (-448000000000 + 537600000000
0*x - 29568000000000*x^2 + 98560000000000*x^3 - 221760000000000*x^4 + 3548160000
00000*x^5 - 413952000000000*x^6 + 354816000000000*x^7 - 221760000000000*x^8 + 98
560000000000*x^9 - 29568000000000*x^10 + 5376000000000*x^11 - 448000000000*x^12)
*#1^12 + (2560000000000 + 2560000000000*E^((140*C[1])/9) - 35840000000000*x + 23
2960000000000*x^2 - 931840000000000*x^3 + 2562560000000000*x^4 - 512512000000000
0*x^5 + 7687680000000000*x^6 - 8785920000000000*x^7 + 7687680000000000*x^8 - 512
5120000000000*x^9 + 2562560000000000*x^10 - 931840000000000*x^11 + 2329600000000
00*x^12 - 35840000000000*x^13 + 2560000000000*x^14)*#1^14 & , 11])}, {y[x] -> (3
*(-1 + x))/7 - 1/(7*Root[1 + (84 - 84*x)*#1 + (2996 - 5992*x + 2996*x^2)*#1^2 +
(57344 - 172032*x + 172032*x^2 - 57344*x^3)*#1^3 + (586656 - 2346624*x + 3519936
*x^2 - 2346624*x^3 + 586656*x^4)*#1^4 + (1993600 - 9968000*x + 19936000*x^2 - 19
936000*x^3 + 9968000*x^4 - 1993600*x^5)*#1^5 + (-21168000 + 127008000*x - 317520
000*x^2 + 423360000*x^3 - 317520000*x^4 + 127008000*x^5 - 21168000*x^6)*#1^6 + (
-247680000 + 1733760000*x - 5201280000*x^2 + 8668800000*x^3 - 8668800000*x^4 + 5
201280000*x^5 - 1733760000*x^6 + 247680000*x^7)*#1^7 + (-453600000 + 3628800000*
x - 12700800000*x^2 + 25401600000*x^3 - 31752000000*x^4 + 25401600000*x^5 - 1270
0800000*x^6 + 3628800000*x^7 - 453600000*x^8)*#1^8 + (5891200000 - 53020800000*x
+ 212083200000*x^2 - 494860800000*x^3 + 742291200000*x^4 - 742291200000*x^5 + 4
94860800000*x^6 - 212083200000*x^7 + 53020800000*x^8 - 5891200000*x^9)*#1^9 + (2
8560000000 - 285600000000*x + 1285200000000*x^2 - 3427200000000*x^3 + 5997600000
000*x^4 - 7197120000000*x^5 + 5997600000000*x^6 - 3427200000000*x^7 + 1285200000
000*x^8 - 285600000000*x^9 + 28560000000*x^10)*#1^10 + (-44800000000 + 492800000
000*x - 2464000000000*x^2 + 7392000000000*x^3 - 14784000000000*x^4 + 20697600000
000*x^5 - 20697600000000*x^6 + 14784000000000*x^7 - 7392000000000*x^8 + 24640000
00000*x^9 - 492800000000*x^10 + 44800000000*x^11)*#1^11 + (-448000000000 + 53760
00000000*x - 29568000000000*x^2 + 98560000000000*x^3 - 221760000000000*x^4 + 354
816000000000*x^5 - 413952000000000*x^6 + 354816000000000*x^7 - 221760000000000*x
^8 + 98560000000000*x^9 - 29568000000000*x^10 + 5376000000000*x^11 - 44800000000
0*x^12)*#1^12 + (2560000000000 + 2560000000000*E^((140*C[1])/9) - 35840000000000
*x + 232960000000000*x^2 - 931840000000000*x^3 + 2562560000000000*x^4 - 51251200
00000000*x^5 + 7687680000000000*x^6 - 8785920000000000*x^7 + 7687680000000000*x^
8 - 5125120000000000*x^9 + 2562560000000000*x^10 - 931840000000000*x^11 + 232960
000000000*x^12 - 35840000000000*x^13 + 2560000000000*x^14)*#1^14 & , 12])}, {y[x
] -> (3*(-1 + x))/7 - 1/(7*Root[1 + (84 - 84*x)*#1 + (2996 - 5992*x + 2996*x^2)*
#1^2 + (57344 - 172032*x + 172032*x^2 - 57344*x^3)*#1^3 + (586656 - 2346624*x +
3519936*x^2 - 2346624*x^3 + 586656*x^4)*#1^4 + (1993600 - 9968000*x + 19936000*x
^2 - 19936000*x^3 + 9968000*x^4 - 1993600*x^5)*#1^5 + (-21168000 + 127008000*x -
317520000*x^2 + 423360000*x^3 - 317520000*x^4 + 127008000*x^5 - 21168000*x^6)*#
1^6 + (-247680000 + 1733760000*x - 5201280000*x^2 + 8668800000*x^3 - 8668800000*
x^4 + 5201280000*x^5 - 1733760000*x^6 + 247680000*x^7)*#1^7 + (-453600000 + 3628
800000*x - 12700800000*x^2 + 25401600000*x^3 - 31752000000*x^4 + 25401600000*x^5
- 12700800000*x^6 + 3628800000*x^7 - 453600000*x^8)*#1^8 + (5891200000 - 530208
00000*x + 212083200000*x^2 - 494860800000*x^3 + 742291200000*x^4 - 742291200000*
x^5 + 494860800000*x^6 - 212083200000*x^7 + 53020800000*x^8 - 5891200000*x^9)*#1
^9 + (28560000000 - 285600000000*x + 1285200000000*x^2 - 3427200000000*x^3 + 599
7600000000*x^4 - 7197120000000*x^5 + 5997600000000*x^6 - 3427200000000*x^7 + 128
5200000000*x^8 - 285600000000*x^9 + 28560000000*x^10)*#1^10 + (-44800000000 + 49
2800000000*x - 2464000000000*x^2 + 7392000000000*x^3 - 14784000000000*x^4 + 2069
7600000000*x^5 - 20697600000000*x^6 + 14784000000000*x^7 - 7392000000000*x^8 + 2
464000000000*x^9 - 492800000000*x^10 + 44800000000*x^11)*#1^11 + (-448000000000
+ 5376000000000*x - 29568000000000*x^2 + 98560000000000*x^3 - 221760000000000*x^
4 + 354816000000000*x^5 - 413952000000000*x^6 + 354816000000000*x^7 - 2217600000
00000*x^8 + 98560000000000*x^9 - 29568000000000*x^10 + 5376000000000*x^11 - 4480
00000000*x^12)*#1^12 + (2560000000000 + 2560000000000*E^((140*C[1])/9) - 3584000
0000000*x + 232960000000000*x^2 - 931840000000000*x^3 + 2562560000000000*x^4 - 5
125120000000000*x^5 + 7687680000000000*x^6 - 8785920000000000*x^7 + 768768000000
0000*x^8 - 5125120000000000*x^9 + 2562560000000000*x^10 - 931840000000000*x^11 +
232960000000000*x^12 - 35840000000000*x^13 + 2560000000000*x^14)*#1^14 & , 13])
}, {y[x] -> (3*(-1 + x))/7 - 1/(7*Root[1 + (84 - 84*x)*#1 + (2996 - 5992*x + 299
6*x^2)*#1^2 + (57344 - 172032*x + 172032*x^2 - 57344*x^3)*#1^3 + (586656 - 23466
24*x + 3519936*x^2 - 2346624*x^3 + 586656*x^4)*#1^4 + (1993600 - 9968000*x + 199
36000*x^2 - 19936000*x^3 + 9968000*x^4 - 1993600*x^5)*#1^5 + (-21168000 + 127008
000*x - 317520000*x^2 + 423360000*x^3 - 317520000*x^4 + 127008000*x^5 - 21168000
*x^6)*#1^6 + (-247680000 + 1733760000*x - 5201280000*x^2 + 8668800000*x^3 - 8668
800000*x^4 + 5201280000*x^5 - 1733760000*x^6 + 247680000*x^7)*#1^7 + (-453600000
+ 3628800000*x - 12700800000*x^2 + 25401600000*x^3 - 31752000000*x^4 + 25401600
000*x^5 - 12700800000*x^6 + 3628800000*x^7 - 453600000*x^8)*#1^8 + (5891200000 -
53020800000*x + 212083200000*x^2 - 494860800000*x^3 + 742291200000*x^4 - 742291
200000*x^5 + 494860800000*x^6 - 212083200000*x^7 + 53020800000*x^8 - 5891200000*
x^9)*#1^9 + (28560000000 - 285600000000*x + 1285200000000*x^2 - 3427200000000*x^
3 + 5997600000000*x^4 - 7197120000000*x^5 + 5997600000000*x^6 - 3427200000000*x^
7 + 1285200000000*x^8 - 285600000000*x^9 + 28560000000*x^10)*#1^10 + (-448000000
00 + 492800000000*x - 2464000000000*x^2 + 7392000000000*x^3 - 14784000000000*x^4
+ 20697600000000*x^5 - 20697600000000*x^6 + 14784000000000*x^7 - 7392000000000*
x^8 + 2464000000000*x^9 - 492800000000*x^10 + 44800000000*x^11)*#1^11 + (-448000
000000 + 5376000000000*x - 29568000000000*x^2 + 98560000000000*x^3 - 22176000000
0000*x^4 + 354816000000000*x^5 - 413952000000000*x^6 + 354816000000000*x^7 - 221
760000000000*x^8 + 98560000000000*x^9 - 29568000000000*x^10 + 5376000000000*x^11
- 448000000000*x^12)*#1^12 + (2560000000000 + 2560000000000*E^((140*C[1])/9) -
35840000000000*x + 232960000000000*x^2 - 931840000000000*x^3 + 2562560000000000*
x^4 - 5125120000000000*x^5 + 7687680000000000*x^6 - 8785920000000000*x^7 + 76876
80000000000*x^8 - 5125120000000000*x^9 + 2562560000000000*x^10 - 931840000000000
*x^11 + 232960000000000*x^12 - 35840000000000*x^13 + 2560000000000*x^14)*#1^14 &
, 14])}}

Maple raw input

dsolve((3-3*x+7*y(x))*diff(y(x),x)+7-7*x+3*y(x) = 0, y(x))

Maple raw output

[y(x) = -(x-1)*(256*RootOf(_Z^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-1
40*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+14
0*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^6-21*_C1*x
^5+35*_C1*x^4-35*_C1*x^3+21*x^2*_C1-7*x*_C1+_C1)^42*_C1^3+432*RootOf(_Z^49+(-4*_
C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*
_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C
1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^6-21*_C1*x^5+35*_C1*x^4-35*_C1*x^3+21*x^2*_C1-7*
x*_C1+_C1)^35*_C1^3+400*RootOf(_Z^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x
^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^
5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^6-21*_
C1*x^5+35*_C1*x^4-35*_C1*x^3+21*x^2*_C1-7*x*_C1+_C1)^28*_C1^3+256*RootOf(_Z^49+(
-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_
C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-2
8*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^6-21*_C1*x^5+35*_C1*x^4-35*_C1*x^3+21*x^2*_C
1-7*x*_C1+_C1)^14*_C1^4*(x-1)^7+220*RootOf(_Z^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x
^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x
^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*
_C1*x^6-21*_C1*x^5+35*_C1*x^4-35*_C1*x^3+21*x^2*_C1-7*x*_C1+_C1)^21*_C1^3+256*Ro
otOf(_Z^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-
28*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+
84*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^6-21*_C1*x^5+35*_C1*x^4-35*_C1*x
^3+21*x^2*_C1-7*x*_C1+_C1)^7*_C1^4*(x-1)^7+72*RootOf(_Z^49+(-4*_C1*x^7+28*_C1*x^
6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^
7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-
_C1*x^7+7*_C1*x^6-21*_C1*x^5+35*_C1*x^4-35*_C1*x^3+21*x^2*_C1-7*x*_C1+_C1)^14*_C
1^3+64*_C1^4*(x-1)^7+13*RootOf(_Z^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x
^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^
5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^6-21*_
C1*x^5+35*_C1*x^4-35*_C1*x^3+21*x^2*_C1-7*x*_C1+_C1)^7*_C1^3+_C1^3)/_C1^3/(192*R
ootOf(_Z^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2
-28*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3
+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^6-21*_C1*x^5+35*_C1*x^4-35*_C1*
x^3+21*x^2*_C1-7*x*_C1+_C1)^42+240*RootOf(_Z^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^
5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^
6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_
C1*x^6-21*_C1*x^5+35*_C1*x^4-35*_C1*x^3+21*x^2*_C1-7*x*_C1+_C1)^35+160*RootOf(_Z
^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*
x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*
x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^6-21*_C1*x^5+35*_C1*x^4-35*_C1*x^3+21*x
^2*_C1-7*x*_C1+_C1)^28+256*RootOf(_Z^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C
1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*_C1
*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^6-2
1*_C1*x^5+35*_C1*x^4-35*_C1*x^3+21*x^2*_C1-7*x*_C1+_C1)^14*_C1*(x-1)^7+60*RootOf
(_Z^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_
C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_
C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^6-21*_C1*x^5+35*_C1*x^4-35*_C1*x^3+2
1*x^2*_C1-7*x*_C1+_C1)^21+256*RootOf(_Z^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140
*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*
_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^
6-21*_C1*x^5+35*_C1*x^4-35*_C1*x^3+21*x^2*_C1-7*x*_C1+_C1)^7*_C1*(x-1)^7+12*Root
Of(_Z^49+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28
*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+28*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84
*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1*x^7+7*_C1*x^6-21*_C1*x^5+35*_C1*x^4-35*_C1*x^3
+21*x^2*_C1-7*x*_C1+_C1)^14+64*(x-1)^7*_C1+RootOf(_Z^49+(-4*_C1*x^7+28*_C1*x^6-8
4*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^14+(-4*_C1*x^7+2
8*_C1*x^6-84*_C1*x^5+140*_C1*x^4-140*_C1*x^3+84*_C1*x^2-28*_C1*x+4*_C1)*_Z^7-_C1
*x^7+7*_C1*x^6-21*_C1*x^5+35*_C1*x^4-35*_C1*x^3+21*x^2*_C1-7*x*_C1+_C1)^7)]

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4.10.47 \((7 y(x)-3 x+3) y'(x)+3 y(x)-7 x+7=0\)