Internal problem ID [3557]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 826.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+x^{4} y^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 38
dsolve(diff(y(x),x)^2-x*y(x)*(x^2+y(x)^2)*diff(y(x),x)+x^4*y(x)^4 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {-x^{2}+c_{1}}} \\ y \relax (x ) = -\frac {1}{\sqrt {-x^{2}+c_{1}}} \\ y \relax (x ) = c_{1} {\mathrm e}^{\frac {x^{4}}{4}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 60
DSolve[(y'[x])^2-x y[x](x^2+y[x]^2)y'[x]+x^4 y[x]^4==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {-x^2-2 c_1}} \\ y(x)\to \frac {1}{\sqrt {-x^2-2 c_1}} \\ y(x)\to c_1 e^{\frac {x^4}{4}} \\ y(x)\to 0 \\ \end{align*}