Internal problem ID [8100]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 520.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{3}+y^{\prime }-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 245
dsolve(diff(y(x),x)^3+diff(y(x),x)-y(x)=0,y(x), singsol=all)
\begin{align*} x -\left (\int _{}^{y \relax (x )}\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 )-c_{1} = 0 \\ x -\left (\int _{}^{y \relax (x )}\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 )-c_{1} = 0 \\ x -\left (\int _{}^{y \relax (x )}-\frac {12 \left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{\frac {1}{3}}}{\left (i \sqrt {3}-1\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 )-c_{1} = 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.313 (sec). Leaf size: 335
DSolve[-y[x] + y'[x] + y'[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}-6 \sqrt [3]{2}}d\text {$\#$1}\&\right ]\left [-\frac {x}{6}+c_1\right ] \\ y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{-i 2^{2/3} \sqrt {3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}-6 i \sqrt [3]{2} \sqrt {3}-6 \sqrt [3]{2}}d\text {$\#$1}\&\right ]\left [\frac {x}{12}+c_1\right ] \\ y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{i 2^{2/3} \sqrt {3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+6 i \sqrt [3]{2} \sqrt {3}-6 \sqrt [3]{2}}d\text {$\#$1}\&\right ]\left [\frac {x}{12}+c_1\right ] \\ y(x)\to 0 \\ \end{align*}