Internal problem ID [3661]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 935.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {x^{4} \left (y^{\prime }\right )^{2}+y^{2} y^{\prime } x -y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.15 (sec). Leaf size: 134
dsolve(x^4*diff(y(x),x)^2+x*y(x)^2*diff(y(x),x)-y(x)^3 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -4 x^{2} \\ y \relax (x ) = 0 \\ y \relax (x ) = \frac {\left (\sqrt {2}\, c_{1}-2 x \right ) c_{1}^{2} x}{2 c_{1}^{2}-4 x^{2}} \\ y \relax (x ) = -\frac {\left (\sqrt {2}\, c_{1}+2 x \right ) c_{1}^{2} x}{2 \left (c_{1}^{2}-2 x^{2}\right )} \\ y \relax (x ) = -\frac {2 \left (\sqrt {2}\, c_{1}-c_{1}^{2} x \right ) x}{c_{1}^{2} \left (c_{1}^{2} x^{2}-2\right )} \\ y \relax (x ) = \frac {2 \left (\sqrt {2}\, c_{1}+c_{1}^{2} x \right ) x}{c_{1}^{2} \left (c_{1}^{2} x^{2}-2\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.62 (sec). Leaf size: 57
DSolve[x^4 (y'[x])^2+x y[x]^2 y'[x]-y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {e^{2 c_1} x}{x+i e^{c_1}} \\ y(x)\to \frac {e^{2 c_1} x}{-x+i e^{c_1}} \\ y(x)\to 0 \\ \end{align*}