Internal problem ID [8118]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 538.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {2 \left (x y^{\prime }+y\right )^{3}-y y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.9 (sec). Leaf size: 3156
dsolve(2*(x*diff(y(x),x)+y(x))^3-y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = 0 \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}
✓ Solution by Mathematica
Time used: 75.546 (sec). Leaf size: 184
DSolve[-(y[x]*y'[x]) + 2*(y[x] + x*y'[x])^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\int _1^x\frac {\text {InverseFunction}\left [-\frac {2 \sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3} \text {ArcTan}\left (\sqrt {8 \text {$\#$1}-1}\right )}{\text {$\#$1} \sqrt {8 \text {$\#$1}-1}}-14 \log \left (\text {$\#$1}^2 (8 \text {$\#$1}-1)\right )+\log \left (\text {$\#$1}^{14} (8 \text {$\#$1}-1)^{15/2} \left (\text {$\#$1}-\sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3}\right )\right )+\log \left (\text {$\#$1}^{12} (8 \text {$\#$1}-1)^{13/2} \left (\text {$\#$1}+\sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3}\right )\right )+\frac {3 \sqrt {\text {$\#$1}^2-8 \text {$\#$1}^3}}{\text {$\#$1}}\&\right ][c_1+2 \log (K[1])]}{K[1]}dK[1]}{x} \\ y(x)\to 0 \\ \end{align*}