Internal problem ID [3555]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 824.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+x y^{2} y^{\prime }+y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.39 (sec). Leaf size: 127
dsolve(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 ) = \frac {4}{x^{2}} \\ y \relax (x ) = 0 \\ y \relax (x ) = \frac {2 \sqrt {2}\, x c_{1}-2 c_{1}^{2}}{c_{1}^{2} \left (-2 x^{2}+c_{1}^{2}\right )} \\ y \relax (x ) = -\frac {2 \left (\sqrt {2}\, x c_{1}+c_{1}^{2}\right )}{c_{1}^{2} \left (-2 x^{2}+c_{1}^{2}\right )} \\ y \relax (x ) = -\frac {\left (\sqrt {2}\, x c_{1}-2\right ) c_{1}^{2}}{2 \left (x^{2} c_{1}^{2}-2\right )} \\ y \relax (x ) = \frac {\left (\sqrt {2}\, x c_{1}+2\right ) c_{1}^{2}}{2 x^{2} c_{1}^{2}-4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.728 (sec). Leaf size: 59
DSolve[(y'[x])^2+x y[x]^2 y'[x]+y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{e^{2 c_1}-i e^{c_1} x} \\ y(x)\to \frac {1}{i e^{c_1} x+e^{2 c_1}} \\ y(x)\to 0 \\ y(x)\to \frac {4}{x^2} \\ \end{align*}