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4.10.50 \((-16 y(x)+7 x+140) y'(x)+y(x)+8 x+25=0\)

ODE
\[ (-16 y(x)+7 x+140) y'(x)+y(x)+8 x+25=0 \] 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 = 0.237379 (sec), leaf count = 1673

\[\left \{\left \{y(x)\to \frac {1}{16} \left (7 (x+20)-\frac {1}{\text {Root}\left [\left (553584375 x^8+17714700000 x^7+248005800000 x^6+1984046400000 x^5+9920232000000 x^4+31744742400000 x^3+63489484800000 x^2+72559411200000 x+553584375 e^{30 c_1}+36279705600000\right ) \text {$\#$1}^8+\left (-16402500 x^6-393660000 x^5-3936600000 x^4-20995200000 x^3-62985600000 x^2-100776960000 x-67184640000\right ) \text {$\#$1}^6+\left (486000 x^5+9720000 x^4+77760000 x^3+311040000 x^2+622080000 x+497664000\right ) \text {$\#$1}^5+\left (166050 x^4+2656800 x^3+15940800 x^2+42508800 x+42508800\right ) \text {$\#$1}^4+\left (-9504 x^3-114048 x^2-456192 x-608256\right ) \text {$\#$1}^3+\left (-468 x^2-3744 x-7488\right ) \text {$\#$1}^2+(48 x+192) \text {$\#$1}-1\& ,1\right ]}\right )\right \},\left \{y(x)\to \frac {1}{16} \left (7 (x+20)-\frac {1}{\text {Root}\left [\left (553584375 x^8+17714700000 x^7+248005800000 x^6+1984046400000 x^5+9920232000000 x^4+31744742400000 x^3+63489484800000 x^2+72559411200000 x+553584375 e^{30 c_1}+36279705600000\right ) \text {$\#$1}^8+\left (-16402500 x^6-393660000 x^5-3936600000 x^4-20995200000 x^3-62985600000 x^2-100776960000 x-67184640000\right ) \text {$\#$1}^6+\left (486000 x^5+9720000 x^4+77760000 x^3+311040000 x^2+622080000 x+497664000\right ) \text {$\#$1}^5+\left (166050 x^4+2656800 x^3+15940800 x^2+42508800 x+42508800\right ) \text {$\#$1}^4+\left (-9504 x^3-114048 x^2-456192 x-608256\right ) \text {$\#$1}^3+\left (-468 x^2-3744 x-7488\right ) \text {$\#$1}^2+(48 x+192) \text {$\#$1}-1\& ,2\right ]}\right )\right \},\left \{y(x)\to \frac {1}{16} \left (7 (x+20)-\frac {1}{\text {Root}\left [\left (553584375 x^8+17714700000 x^7+248005800000 x^6+1984046400000 x^5+9920232000000 x^4+31744742400000 x^3+63489484800000 x^2+72559411200000 x+553584375 e^{30 c_1}+36279705600000\right ) \text {$\#$1}^8+\left (-16402500 x^6-393660000 x^5-3936600000 x^4-20995200000 x^3-62985600000 x^2-100776960000 x-67184640000\right ) \text {$\#$1}^6+\left (486000 x^5+9720000 x^4+77760000 x^3+311040000 x^2+622080000 x+497664000\right ) \text {$\#$1}^5+\left (166050 x^4+2656800 x^3+15940800 x^2+42508800 x+42508800\right ) \text {$\#$1}^4+\left (-9504 x^3-114048 x^2-456192 x-608256\right ) \text {$\#$1}^3+\left (-468 x^2-3744 x-7488\right ) \text {$\#$1}^2+(48 x+192) \text {$\#$1}-1\& ,3\right ]}\right )\right \},\left \{y(x)\to \frac {1}{16} \left (7 (x+20)-\frac {1}{\text {Root}\left [\left (553584375 x^8+17714700000 x^7+248005800000 x^6+1984046400000 x^5+9920232000000 x^4+31744742400000 x^3+63489484800000 x^2+72559411200000 x+553584375 e^{30 c_1}+36279705600000\right ) \text {$\#$1}^8+\left (-16402500 x^6-393660000 x^5-3936600000 x^4-20995200000 x^3-62985600000 x^2-100776960000 x-67184640000\right ) \text {$\#$1}^6+\left (486000 x^5+9720000 x^4+77760000 x^3+311040000 x^2+622080000 x+497664000\right ) \text {$\#$1}^5+\left (166050 x^4+2656800 x^3+15940800 x^2+42508800 x+42508800\right ) \text {$\#$1}^4+\left (-9504 x^3-114048 x^2-456192 x-608256\right ) \text {$\#$1}^3+\left (-468 x^2-3744 x-7488\right ) \text {$\#$1}^2+(48 x+192) \text {$\#$1}-1\& ,4\right ]}\right )\right \},\left \{y(x)\to \frac {1}{16} \left (7 (x+20)-\frac {1}{\text {Root}\left [\left (553584375 x^8+17714700000 x^7+248005800000 x^6+1984046400000 x^5+9920232000000 x^4+31744742400000 x^3+63489484800000 x^2+72559411200000 x+553584375 e^{30 c_1}+36279705600000\right ) \text {$\#$1}^8+\left (-16402500 x^6-393660000 x^5-3936600000 x^4-20995200000 x^3-62985600000 x^2-100776960000 x-67184640000\right ) \text {$\#$1}^6+\left (486000 x^5+9720000 x^4+77760000 x^3+311040000 x^2+622080000 x+497664000\right ) \text {$\#$1}^5+\left (166050 x^4+2656800 x^3+15940800 x^2+42508800 x+42508800\right ) \text {$\#$1}^4+\left (-9504 x^3-114048 x^2-456192 x-608256\right ) \text {$\#$1}^3+\left (-468 x^2-3744 x-7488\right ) \text {$\#$1}^2+(48 x+192) \text {$\#$1}-1\& ,5\right ]}\right )\right \},\left \{y(x)\to \frac {1}{16} \left (7 (x+20)-\frac {1}{\text {Root}\left [\left (553584375 x^8+17714700000 x^7+248005800000 x^6+1984046400000 x^5+9920232000000 x^4+31744742400000 x^3+63489484800000 x^2+72559411200000 x+553584375 e^{30 c_1}+36279705600000\right ) \text {$\#$1}^8+\left (-16402500 x^6-393660000 x^5-3936600000 x^4-20995200000 x^3-62985600000 x^2-100776960000 x-67184640000\right ) \text {$\#$1}^6+\left (486000 x^5+9720000 x^4+77760000 x^3+311040000 x^2+622080000 x+497664000\right ) \text {$\#$1}^5+\left (166050 x^4+2656800 x^3+15940800 x^2+42508800 x+42508800\right ) \text {$\#$1}^4+\left (-9504 x^3-114048 x^2-456192 x-608256\right ) \text {$\#$1}^3+\left (-468 x^2-3744 x-7488\right ) \text {$\#$1}^2+(48 x+192) \text {$\#$1}-1\& ,6\right ]}\right )\right \},\left \{y(x)\to \frac {1}{16} \left (7 (x+20)-\frac {1}{\text {Root}\left [\left (553584375 x^8+17714700000 x^7+248005800000 x^6+1984046400000 x^5+9920232000000 x^4+31744742400000 x^3+63489484800000 x^2+72559411200000 x+553584375 e^{30 c_1}+36279705600000\right ) \text {$\#$1}^8+\left (-16402500 x^6-393660000 x^5-3936600000 x^4-20995200000 x^3-62985600000 x^2-100776960000 x-67184640000\right ) \text {$\#$1}^6+\left (486000 x^5+9720000 x^4+77760000 x^3+311040000 x^2+622080000 x+497664000\right ) \text {$\#$1}^5+\left (166050 x^4+2656800 x^3+15940800 x^2+42508800 x+42508800\right ) \text {$\#$1}^4+\left (-9504 x^3-114048 x^2-456192 x-608256\right ) \text {$\#$1}^3+\left (-468 x^2-3744 x-7488\right ) \text {$\#$1}^2+(48 x+192) \text {$\#$1}-1\& ,7\right ]}\right )\right \},\left \{y(x)\to \frac {1}{16} \left (7 (x+20)-\frac {1}{\text {Root}\left [\left (553584375 x^8+17714700000 x^7+248005800000 x^6+1984046400000 x^5+9920232000000 x^4+31744742400000 x^3+63489484800000 x^2+72559411200000 x+553584375 e^{30 c_1}+36279705600000\right ) \text {$\#$1}^8+\left (-16402500 x^6-393660000 x^5-3936600000 x^4-20995200000 x^3-62985600000 x^2-100776960000 x-67184640000\right ) \text {$\#$1}^6+\left (486000 x^5+9720000 x^4+77760000 x^3+311040000 x^2+622080000 x+497664000\right ) \text {$\#$1}^5+\left (166050 x^4+2656800 x^3+15940800 x^2+42508800 x+42508800\right ) \text {$\#$1}^4+\left (-9504 x^3-114048 x^2-456192 x-608256\right ) \text {$\#$1}^3+\left (-468 x^2-3744 x-7488\right ) \text {$\#$1}^2+(48 x+192) \text {$\#$1}-1\& ,8\right ]}\right )\right \}\right \}\]

Maple ✓
cpu = 0.347 (sec), leaf count = 1366

\[\left [y \left (x \right ) = 7-\frac {-\left (4+x \right )^{8} \RootOf \left (-8+\left (\textit {\_C1} \,x^{8}+32 \textit {\_C1} \,x^{7}+448 \textit {\_C1} \,x^{6}+3584 \textit {\_C1} \,x^{5}+17920 \textit {\_C1} \,x^{4}+57344 \textit {\_C1} \,x^{3}+114688 x^{2} \textit {\_C1} +131072 x \textit {\_C1} +65536 \textit {\_C1} \right ) \textit {\_Z}^{64}+\left (9 \textit {\_C1} \,x^{8}+288 \textit {\_C1} \,x^{7}+4032 \textit {\_C1} \,x^{6}+32256 \textit {\_C1} \,x^{5}+161280 \textit {\_C1} \,x^{4}+516096 \textit {\_C1} \,x^{3}+1032192 x^{2} \textit {\_C1} +1179648 x \textit {\_C1} +589824 \textit {\_C1} \right ) \textit {\_Z}^{56}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{48}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{40}\right )^{56}-6 \left (4+x \right )^{8} \RootOf \left (-8+\left (\textit {\_C1} \,x^{8}+32 \textit {\_C1} \,x^{7}+448 \textit {\_C1} \,x^{6}+3584 \textit {\_C1} \,x^{5}+17920 \textit {\_C1} \,x^{4}+57344 \textit {\_C1} \,x^{3}+114688 x^{2} \textit {\_C1} +131072 x \textit {\_C1} +65536 \textit {\_C1} \right ) \textit {\_Z}^{64}+\left (9 \textit {\_C1} \,x^{8}+288 \textit {\_C1} \,x^{7}+4032 \textit {\_C1} \,x^{6}+32256 \textit {\_C1} \,x^{5}+161280 \textit {\_C1} \,x^{4}+516096 \textit {\_C1} \,x^{3}+1032192 x^{2} \textit {\_C1} +1179648 x \textit {\_C1} +589824 \textit {\_C1} \right ) \textit {\_Z}^{56}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{48}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{40}\right )^{48}-9 \left (4+x \right )^{8} \RootOf \left (-8+\left (\textit {\_C1} \,x^{8}+32 \textit {\_C1} \,x^{7}+448 \textit {\_C1} \,x^{6}+3584 \textit {\_C1} \,x^{5}+17920 \textit {\_C1} \,x^{4}+57344 \textit {\_C1} \,x^{3}+114688 x^{2} \textit {\_C1} +131072 x \textit {\_C1} +65536 \textit {\_C1} \right ) \textit {\_Z}^{64}+\left (9 \textit {\_C1} \,x^{8}+288 \textit {\_C1} \,x^{7}+4032 \textit {\_C1} \,x^{6}+32256 \textit {\_C1} \,x^{5}+161280 \textit {\_C1} \,x^{4}+516096 \textit {\_C1} \,x^{3}+1032192 x^{2} \textit {\_C1} +1179648 x \textit {\_C1} +589824 \textit {\_C1} \right ) \textit {\_Z}^{56}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{48}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{40}\right )^{40}+\frac {4}{\textit {\_C1}}}{\left (4+x \right )^{7} \RootOf \left (-8+\left (\textit {\_C1} \,x^{8}+32 \textit {\_C1} \,x^{7}+448 \textit {\_C1} \,x^{6}+3584 \textit {\_C1} \,x^{5}+17920 \textit {\_C1} \,x^{4}+57344 \textit {\_C1} \,x^{3}+114688 x^{2} \textit {\_C1} +131072 x \textit {\_C1} +65536 \textit {\_C1} \right ) \textit {\_Z}^{64}+\left (9 \textit {\_C1} \,x^{8}+288 \textit {\_C1} \,x^{7}+4032 \textit {\_C1} \,x^{6}+32256 \textit {\_C1} \,x^{5}+161280 \textit {\_C1} \,x^{4}+516096 \textit {\_C1} \,x^{3}+1032192 x^{2} \textit {\_C1} +1179648 x \textit {\_C1} +589824 \textit {\_C1} \right ) \textit {\_Z}^{56}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{48}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{40}\right )^{40} \left (\RootOf \left (-8+\left (\textit {\_C1} \,x^{8}+32 \textit {\_C1} \,x^{7}+448 \textit {\_C1} \,x^{6}+3584 \textit {\_C1} \,x^{5}+17920 \textit {\_C1} \,x^{4}+57344 \textit {\_C1} \,x^{3}+114688 x^{2} \textit {\_C1} +131072 x \textit {\_C1} +65536 \textit {\_C1} \right ) \textit {\_Z}^{64}+\left (9 \textit {\_C1} \,x^{8}+288 \textit {\_C1} \,x^{7}+4032 \textit {\_C1} \,x^{6}+32256 \textit {\_C1} \,x^{5}+161280 \textit {\_C1} \,x^{4}+516096 \textit {\_C1} \,x^{3}+1032192 x^{2} \textit {\_C1} +1179648 x \textit {\_C1} +589824 \textit {\_C1} \right ) \textit {\_Z}^{56}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{48}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{40}\right )^{16}+6 \RootOf \left (-8+\left (\textit {\_C1} \,x^{8}+32 \textit {\_C1} \,x^{7}+448 \textit {\_C1} \,x^{6}+3584 \textit {\_C1} \,x^{5}+17920 \textit {\_C1} \,x^{4}+57344 \textit {\_C1} \,x^{3}+114688 x^{2} \textit {\_C1} +131072 x \textit {\_C1} +65536 \textit {\_C1} \right ) \textit {\_Z}^{64}+\left (9 \textit {\_C1} \,x^{8}+288 \textit {\_C1} \,x^{7}+4032 \textit {\_C1} \,x^{6}+32256 \textit {\_C1} \,x^{5}+161280 \textit {\_C1} \,x^{4}+516096 \textit {\_C1} \,x^{3}+1032192 x^{2} \textit {\_C1} +1179648 x \textit {\_C1} +589824 \textit {\_C1} \right ) \textit {\_Z}^{56}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{48}+\left (27 \textit {\_C1} \,x^{8}+864 \textit {\_C1} \,x^{7}+12096 \textit {\_C1} \,x^{6}+96768 \textit {\_C1} \,x^{5}+483840 \textit {\_C1} \,x^{4}+1548288 \textit {\_C1} \,x^{3}+3096576 x^{2} \textit {\_C1} +3538944 x \textit {\_C1} +1769472 \textit {\_C1} \right ) \textit {\_Z}^{40}\right )^{8}+9\right )}\right ]\] Mathematica raw input

DSolve[25 + 8*x + y[x] + (140 + 7*x - 16*y[x])*y'[x] == 0,y[x],x]

Mathematica raw output

{{y[x] -> (7*(20 + x) - Root[-1 + (192 + 48*x)*#1 + (-7488 - 3744*x - 468*x^2)*#
1^2 + (-608256 - 456192*x - 114048*x^2 - 9504*x^3)*#1^3 + (42508800 + 42508800*x
 + 15940800*x^2 + 2656800*x^3 + 166050*x^4)*#1^4 + (497664000 + 622080000*x + 31
1040000*x^2 + 77760000*x^3 + 9720000*x^4 + 486000*x^5)*#1^5 + (-67184640000 - 10
0776960000*x - 62985600000*x^2 - 20995200000*x^3 - 3936600000*x^4 - 393660000*x^
5 - 16402500*x^6)*#1^6 + (36279705600000 + 553584375*E^(30*C[1]) + 7255941120000
0*x + 63489484800000*x^2 + 31744742400000*x^3 + 9920232000000*x^4 + 198404640000
0*x^5 + 248005800000*x^6 + 17714700000*x^7 + 553584375*x^8)*#1^8 & , 1]^(-1))/16
}, {y[x] -> (7*(20 + x) - Root[-1 + (192 + 48*x)*#1 + (-7488 - 3744*x - 468*x^2)
*#1^2 + (-608256 - 456192*x - 114048*x^2 - 9504*x^3)*#1^3 + (42508800 + 42508800
*x + 15940800*x^2 + 2656800*x^3 + 166050*x^4)*#1^4 + (497664000 + 622080000*x + 
311040000*x^2 + 77760000*x^3 + 9720000*x^4 + 486000*x^5)*#1^5 + (-67184640000 - 
100776960000*x - 62985600000*x^2 - 20995200000*x^3 - 3936600000*x^4 - 393660000*
x^5 - 16402500*x^6)*#1^6 + (36279705600000 + 553584375*E^(30*C[1]) + 72559411200
000*x + 63489484800000*x^2 + 31744742400000*x^3 + 9920232000000*x^4 + 1984046400
000*x^5 + 248005800000*x^6 + 17714700000*x^7 + 553584375*x^8)*#1^8 & , 2]^(-1))/
16}, {y[x] -> (7*(20 + x) - Root[-1 + (192 + 48*x)*#1 + (-7488 - 3744*x - 468*x^
2)*#1^2 + (-608256 - 456192*x - 114048*x^2 - 9504*x^3)*#1^3 + (42508800 + 425088
00*x + 15940800*x^2 + 2656800*x^3 + 166050*x^4)*#1^4 + (497664000 + 622080000*x 
+ 311040000*x^2 + 77760000*x^3 + 9720000*x^4 + 486000*x^5)*#1^5 + (-67184640000 
- 100776960000*x - 62985600000*x^2 - 20995200000*x^3 - 3936600000*x^4 - 39366000
0*x^5 - 16402500*x^6)*#1^6 + (36279705600000 + 553584375*E^(30*C[1]) + 725594112
00000*x + 63489484800000*x^2 + 31744742400000*x^3 + 9920232000000*x^4 + 19840464
00000*x^5 + 248005800000*x^6 + 17714700000*x^7 + 553584375*x^8)*#1^8 & , 3]^(-1)
)/16}, {y[x] -> (7*(20 + x) - Root[-1 + (192 + 48*x)*#1 + (-7488 - 3744*x - 468*
x^2)*#1^2 + (-608256 - 456192*x - 114048*x^2 - 9504*x^3)*#1^3 + (42508800 + 4250
8800*x + 15940800*x^2 + 2656800*x^3 + 166050*x^4)*#1^4 + (497664000 + 622080000*
x + 311040000*x^2 + 77760000*x^3 + 9720000*x^4 + 486000*x^5)*#1^5 + (-6718464000
0 - 100776960000*x - 62985600000*x^2 - 20995200000*x^3 - 3936600000*x^4 - 393660
000*x^5 - 16402500*x^6)*#1^6 + (36279705600000 + 553584375*E^(30*C[1]) + 7255941
1200000*x + 63489484800000*x^2 + 31744742400000*x^3 + 9920232000000*x^4 + 198404
6400000*x^5 + 248005800000*x^6 + 17714700000*x^7 + 553584375*x^8)*#1^8 & , 4]^(-
1))/16}, {y[x] -> (7*(20 + x) - Root[-1 + (192 + 48*x)*#1 + (-7488 - 3744*x - 46
8*x^2)*#1^2 + (-608256 - 456192*x - 114048*x^2 - 9504*x^3)*#1^3 + (42508800 + 42
508800*x + 15940800*x^2 + 2656800*x^3 + 166050*x^4)*#1^4 + (497664000 + 62208000
0*x + 311040000*x^2 + 77760000*x^3 + 9720000*x^4 + 486000*x^5)*#1^5 + (-67184640
000 - 100776960000*x - 62985600000*x^2 - 20995200000*x^3 - 3936600000*x^4 - 3936
60000*x^5 - 16402500*x^6)*#1^6 + (36279705600000 + 553584375*E^(30*C[1]) + 72559
411200000*x + 63489484800000*x^2 + 31744742400000*x^3 + 9920232000000*x^4 + 1984
046400000*x^5 + 248005800000*x^6 + 17714700000*x^7 + 553584375*x^8)*#1^8 & , 5]^
(-1))/16}, {y[x] -> (7*(20 + x) - Root[-1 + (192 + 48*x)*#1 + (-7488 - 3744*x - 
468*x^2)*#1^2 + (-608256 - 456192*x - 114048*x^2 - 9504*x^3)*#1^3 + (42508800 + 
42508800*x + 15940800*x^2 + 2656800*x^3 + 166050*x^4)*#1^4 + (497664000 + 622080
000*x + 311040000*x^2 + 77760000*x^3 + 9720000*x^4 + 486000*x^5)*#1^5 + (-671846
40000 - 100776960000*x - 62985600000*x^2 - 20995200000*x^3 - 3936600000*x^4 - 39
3660000*x^5 - 16402500*x^6)*#1^6 + (36279705600000 + 553584375*E^(30*C[1]) + 725
59411200000*x + 63489484800000*x^2 + 31744742400000*x^3 + 9920232000000*x^4 + 19
84046400000*x^5 + 248005800000*x^6 + 17714700000*x^7 + 553584375*x^8)*#1^8 & , 6
]^(-1))/16}, {y[x] -> (7*(20 + x) - Root[-1 + (192 + 48*x)*#1 + (-7488 - 3744*x 
- 468*x^2)*#1^2 + (-608256 - 456192*x - 114048*x^2 - 9504*x^3)*#1^3 + (42508800 
+ 42508800*x + 15940800*x^2 + 2656800*x^3 + 166050*x^4)*#1^4 + (497664000 + 6220
80000*x + 311040000*x^2 + 77760000*x^3 + 9720000*x^4 + 486000*x^5)*#1^5 + (-6718
4640000 - 100776960000*x - 62985600000*x^2 - 20995200000*x^3 - 3936600000*x^4 - 
393660000*x^5 - 16402500*x^6)*#1^6 + (36279705600000 + 553584375*E^(30*C[1]) + 7
2559411200000*x + 63489484800000*x^2 + 31744742400000*x^3 + 9920232000000*x^4 + 
1984046400000*x^5 + 248005800000*x^6 + 17714700000*x^7 + 553584375*x^8)*#1^8 & ,
 7]^(-1))/16}, {y[x] -> (7*(20 + x) - Root[-1 + (192 + 48*x)*#1 + (-7488 - 3744*
x - 468*x^2)*#1^2 + (-608256 - 456192*x - 114048*x^2 - 9504*x^3)*#1^3 + (4250880
0 + 42508800*x + 15940800*x^2 + 2656800*x^3 + 166050*x^4)*#1^4 + (497664000 + 62
2080000*x + 311040000*x^2 + 77760000*x^3 + 9720000*x^4 + 486000*x^5)*#1^5 + (-67
184640000 - 100776960000*x - 62985600000*x^2 - 20995200000*x^3 - 3936600000*x^4 
- 393660000*x^5 - 16402500*x^6)*#1^6 + (36279705600000 + 553584375*E^(30*C[1]) +
 72559411200000*x + 63489484800000*x^2 + 31744742400000*x^3 + 9920232000000*x^4 
+ 1984046400000*x^5 + 248005800000*x^6 + 17714700000*x^7 + 553584375*x^8)*#1^8 &
 , 8]^(-1))/16}}

Maple raw input

dsolve((140+7*x-16*y(x))*diff(y(x),x)+25+8*x+y(x) = 0, y(x))

Maple raw output

[y(x) = 7-(-(4+x)^8*RootOf(-8+(_C1*x^8+32*_C1*x^7+448*_C1*x^6+3584*_C1*x^5+17920
*_C1*x^4+57344*_C1*x^3+114688*_C1*x^2+131072*_C1*x+65536*_C1)*_Z^64+(9*_C1*x^8+2
88*_C1*x^7+4032*_C1*x^6+32256*_C1*x^5+161280*_C1*x^4+516096*_C1*x^3+1032192*_C1*
x^2+1179648*_C1*x+589824*_C1)*_Z^56+(27*_C1*x^8+864*_C1*x^7+12096*_C1*x^6+96768*
_C1*x^5+483840*_C1*x^4+1548288*_C1*x^3+3096576*_C1*x^2+3538944*_C1*x+1769472*_C1
)*_Z^48+(27*_C1*x^8+864*_C1*x^7+12096*_C1*x^6+96768*_C1*x^5+483840*_C1*x^4+15482
88*_C1*x^3+3096576*_C1*x^2+3538944*_C1*x+1769472*_C1)*_Z^40)^56-6*(4+x)^8*RootOf
(-8+(_C1*x^8+32*_C1*x^7+448*_C1*x^6+3584*_C1*x^5+17920*_C1*x^4+57344*_C1*x^3+114
688*_C1*x^2+131072*_C1*x+65536*_C1)*_Z^64+(9*_C1*x^8+288*_C1*x^7+4032*_C1*x^6+32
256*_C1*x^5+161280*_C1*x^4+516096*_C1*x^3+1032192*_C1*x^2+1179648*_C1*x+589824*_
C1)*_Z^56+(27*_C1*x^8+864*_C1*x^7+12096*_C1*x^6+96768*_C1*x^5+483840*_C1*x^4+154
8288*_C1*x^3+3096576*_C1*x^2+3538944*_C1*x+1769472*_C1)*_Z^48+(27*_C1*x^8+864*_C
1*x^7+12096*_C1*x^6+96768*_C1*x^5+483840*_C1*x^4+1548288*_C1*x^3+3096576*_C1*x^2
+3538944*_C1*x+1769472*_C1)*_Z^40)^48-9*(4+x)^8*RootOf(-8+(_C1*x^8+32*_C1*x^7+44
8*_C1*x^6+3584*_C1*x^5+17920*_C1*x^4+57344*_C1*x^3+114688*_C1*x^2+131072*_C1*x+6
5536*_C1)*_Z^64+(9*_C1*x^8+288*_C1*x^7+4032*_C1*x^6+32256*_C1*x^5+161280*_C1*x^4
+516096*_C1*x^3+1032192*_C1*x^2+1179648*_C1*x+589824*_C1)*_Z^56+(27*_C1*x^8+864*
_C1*x^7+12096*_C1*x^6+96768*_C1*x^5+483840*_C1*x^4+1548288*_C1*x^3+3096576*_C1*x
^2+3538944*_C1*x+1769472*_C1)*_Z^48+(27*_C1*x^8+864*_C1*x^7+12096*_C1*x^6+96768*
_C1*x^5+483840*_C1*x^4+1548288*_C1*x^3+3096576*_C1*x^2+3538944*_C1*x+1769472*_C1
)*_Z^40)^40+4/_C1)/(4+x)^7/RootOf(-8+(_C1*x^8+32*_C1*x^7+448*_C1*x^6+3584*_C1*x^
5+17920*_C1*x^4+57344*_C1*x^3+114688*_C1*x^2+131072*_C1*x+65536*_C1)*_Z^64+(9*_C
1*x^8+288*_C1*x^7+4032*_C1*x^6+32256*_C1*x^5+161280*_C1*x^4+516096*_C1*x^3+10321
92*_C1*x^2+1179648*_C1*x+589824*_C1)*_Z^56+(27*_C1*x^8+864*_C1*x^7+12096*_C1*x^6
+96768*_C1*x^5+483840*_C1*x^4+1548288*_C1*x^3+3096576*_C1*x^2+3538944*_C1*x+1769
472*_C1)*_Z^48+(27*_C1*x^8+864*_C1*x^7+12096*_C1*x^6+96768*_C1*x^5+483840*_C1*x^
4+1548288*_C1*x^3+3096576*_C1*x^2+3538944*_C1*x+1769472*_C1)*_Z^40)^40/(RootOf(-
8+(_C1*x^8+32*_C1*x^7+448*_C1*x^6+3584*_C1*x^5+17920*_C1*x^4+57344*_C1*x^3+11468
8*_C1*x^2+131072*_C1*x+65536*_C1)*_Z^64+(9*_C1*x^8+288*_C1*x^7+4032*_C1*x^6+3225
6*_C1*x^5+161280*_C1*x^4+516096*_C1*x^3+1032192*_C1*x^2+1179648*_C1*x+589824*_C1
)*_Z^56+(27*_C1*x^8+864*_C1*x^7+12096*_C1*x^6+96768*_C1*x^5+483840*_C1*x^4+15482
88*_C1*x^3+3096576*_C1*x^2+3538944*_C1*x+1769472*_C1)*_Z^48+(27*_C1*x^8+864*_C1*
x^7+12096*_C1*x^6+96768*_C1*x^5+483840*_C1*x^4+1548288*_C1*x^3+3096576*_C1*x^2+3
538944*_C1*x+1769472*_C1)*_Z^40)^16+6*RootOf(-8+(_C1*x^8+32*_C1*x^7+448*_C1*x^6+
3584*_C1*x^5+17920*_C1*x^4+57344*_C1*x^3+114688*_C1*x^2+131072*_C1*x+65536*_C1)*
_Z^64+(9*_C1*x^8+288*_C1*x^7+4032*_C1*x^6+32256*_C1*x^5+161280*_C1*x^4+516096*_C
1*x^3+1032192*_C1*x^2+1179648*_C1*x+589824*_C1)*_Z^56+(27*_C1*x^8+864*_C1*x^7+12
096*_C1*x^6+96768*_C1*x^5+483840*_C1*x^4+1548288*_C1*x^3+3096576*_C1*x^2+3538944
*_C1*x+1769472*_C1)*_Z^48+(27*_C1*x^8+864*_C1*x^7+12096*_C1*x^6+96768*_C1*x^5+48
3840*_C1*x^4+1548288*_C1*x^3+3096576*_C1*x^2+3538944*_C1*x+1769472*_C1)*_Z^40)^8
+9)]

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