ODE
\[ y'(x)^3+y'(x)-y(x)=0 \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Independent variable missing, Solve for \(y\)
Mathematica ✓
cpu = 0.172507 (sec), leaf count = 1115
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}}{0\ 2 \sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}+2^{2/3} \left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9\right )^{2/3}+2\ 0^2 \sqrt [3]{2}-6 \sqrt [3]{2}}d\text {$\#$1}\& \right ]\left [c_1-\frac {x}{6}\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}}{-0 4 \sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}+2^{2/3} \left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9\right )^{2/3}-2^{2/3} i \sqrt {3} \left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9\right )^{2/3}+2\ 0^2 \sqrt [3]{2}-6 \sqrt [3]{2}+2\ 0^2 \sqrt [3]{2} i \sqrt {3}-6 \sqrt [3]{2} i \sqrt {3}}d\text {$\#$1}\& \right ]\left [\frac {x}{12}+c_1\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}}{-0 4 \sqrt [3]{-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9}+2^{2/3} \left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9\right )^{2/3}+2^{2/3} i \sqrt {3} \left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2+\sqrt {4 \left (-0^2+3\ 1\ 1\right )^3+\left (-27 1^2 \text {$\#$1}+2\ 0^3-0\ 27\ 1^2-0\ 9\right )^2}-0\ 9\right )^{2/3}+2\ 0^2 \sqrt [3]{2}-6 \sqrt [3]{2}-2\ 0^2 \sqrt [3]{2} i \sqrt {3}+6 \sqrt [3]{2} i \sqrt {3}}d\text {$\#$1}\& \right ]\left [\frac {x}{12}+c_1\right ]\right \}\right \}\]
Maple ✓
cpu = 0.588 (sec), leaf count = 249
\[\left [x -\left (\int _{}^{y \left (x \right )}\frac {6 \left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {1}{3}}}{\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {2}{3}}-12}d \textit {\_a} \right )-\textit {\_C1} = 0, x -\left (\int _{}^{y \left (x \right )}\frac {12 \left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {1}{3}}}{\left (1+i \sqrt {3}\right ) \left (\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {1}{3}}-\sqrt {3}+3 i\right ) \left (-\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {1}{3}}+3 i-\sqrt {3}\right )}d \textit {\_a} \right )-\textit {\_C1} = 0, x -\left (\int _{}^{y \left (x \right )}-\frac {12 \left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {1}{3}}}{\left (-1+i \sqrt {3}\right ) \left (-\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {1}{3}}+\sqrt {3}+3 i\right ) \left (\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {1}{3}}+3 i+\sqrt {3}\right )}d \textit {\_a} \right )-\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[-y[x] + y'[x] + y'[x]^3 == 0,y[x],x]
Mathematica raw output
{{y[x] -> InverseFunction[Inactive[Integrate][(2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1 + Sqrt[4*(-0^2 + 3*1*1)^3 + (2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1)^2])^(1/3)/(2*2^(1/3)*0^2 - 6*2^(1/3)*1*1 + 2*0*(2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1 + Sqrt[4*(-0^2 + 3*1*1)^3 + (2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1)^2])^(1/3) + 2^(2/3)*(2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1 + Sqrt[4*(-0^2 + 3*1*1)^3 + (2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1)^2])^(2/3)), #1] & ][-1/6*x + C[1]]}, {y[x] -> InverseFunction[Inactive[Integrate][(2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1 + Sqrt[4*(-0^2 + 3*1*1)^3 + (2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1)^2])^(1/3)/(2*2^(1/3)*0^2 + 2*I*2^(1/3)*Sqrt[3]*0^2 - 6*2^(1/3)*1*1 - 6*I*2^(1/3)*Sqrt[3]*1*1 - 4*0*(2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1 + Sqrt[4*(-0^2 + 3*1*1)^3 + (2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1)^2])^(1/3) + 2^(2/3)*(2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1 + Sqrt[4*(-0^2 + 3*1*1)^3 + (2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1)^2])^(2/3) - I*2^(2/3)*Sqrt[3]*(2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1 + Sqrt[4*(-0^2 + 3*1*1)^3 + (2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1)^2])^(2/3)), #1] & ][x/12 + C[1]]}, {y[x] -> InverseFunction[Inactive[Integrate][(2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1 + Sqrt[4*(-0^2 + 3*1*1)^3 + (2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1)^2])^(1/3)/(2*2^(1/3)*0^2 - 2*I*2^(1/3)*Sqrt[3]*0^2 - 6*2^(1/3)*1*1 + 6*I*2^(1/3)*Sqrt[3]*1*1 - 4*0*(2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1 + Sqrt[4*(-0^2 + 3*1*1)^3 + (2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1)^2])^(1/3) + 2^(2/3)*(2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1 + Sqrt[4*(-0^2 + 3*1*1)^3 + (2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1)^2])^(2/3) + I*2^(2/3)*Sqrt[3]*(2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1 + Sqrt[4*(-0^2 + 3*1*1)^3 + (2*0^3 - 9*1*0*1 - 27*1^2*0 - 27*1^2*#1)^2])^(2/3)), #1] & ][x/12 + C[1]]}}
Maple raw input
dsolve(diff(y(x),x)^3+diff(y(x),x)-y(x) = 0, y(x))
Maple raw output
[x-Intat(6/((108*_a+12*(81*_a^2+12)^(1/2))^(2/3)-12)*(108*_a+12*(81*_a^2+12)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(12/(1+I*3^(1/2))/((108*_a+12*(81*_a^2+12)^(1/2))^(1/3)-3^(1/2)+3*I)/(-(108*_a+12*(81*_a^2+12)^(1/2))^(1/3)+3*I-3^(1/2))*(108*_a+12*(81*_a^2+12)^(1/2))^(1/3),_a = y(x))-_C1 = 0, x-Intat(-12/(-1+I*3^(1/2))/(-(108*_a+12*(81*_a^2+12)^(1/2))^(1/3)+3^(1/2)+3*I)/((108*_a+12*(81*_a^2+12)^(1/2))^(1/3)+3*I+3^(1/2))*(108*_a+12*(81*_a^2+12)^(1/2))^(1/3),_a = y(x))-_C1 = 0]