Internal problem ID [4169]
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`]]
\[ \boxed {x^{4} {y^{\prime }}^{2}+x y^{2} y^{\prime }-y^{3}=0} \]
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 129
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 \left (x \right ) &= -4 x^{2} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (\sqrt {2}\, c_{1} -2 x \right ) c_{1}^{2} x}{2 c_{1}^{2}-4 x^{2}} \\ y \left (x \right ) &= -\frac {\left (\sqrt {2}\, c_{1} +2 x \right ) c_{1}^{2} x}{2 c_{1}^{2}-4 x^{2}} \\ y \left (x \right ) &= -\frac {2 \left (-c_{1} x +\sqrt {2}\right ) x}{c_{1} \left (c_{1}^{2} x^{2}-2\right )} \\ y \left (x \right ) &= \frac {2 \left (c_{1} x +\sqrt {2}\right ) x}{c_{1} \left (c_{1}^{2} x^{2}-2\right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.844 (sec). Leaf size: 79
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 {x (\cosh (2 c_1)+\sinh (2 c_1))}{x+i \cosh (c_1)+i \sinh (c_1)} \\ y(x)\to \frac {x (\cosh (2 c_1)+\sinh (2 c_1))}{-x+i \cosh (c_1)+i \sinh (c_1)} \\ y(x)\to 0 \\ \end{align*}