Internal problem ID [3780]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 36
Problem number: 1068.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {2 x^{3} \left (y^{\prime }\right )^{3}+6 x^{2} y \left (y^{\prime }\right )^{2}-\left (1-6 y x \right ) y y^{\prime }+2 y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.931 (sec). Leaf size: 3159
dsolve(2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2*y(x)^3 = 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: 76.762 (sec). Leaf size: 184
DSolve[2 x^3 (y'[x])^3 +6 x^2 y[x] (y'[x])^2 -(1-6 x y[x])y[x] y'[x]+2 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*}