Internal problem ID [3727]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 34
Problem number: 1004.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {4 x^{2} y^{2} \left (y^{\prime }\right )^{2}-\left (x^{2}+y^{2}\right )^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 75
dsolve(4*x^2*y(x)^2*diff(y(x),x)^2 = (x^2+y(x)^2)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = \sqrt {x^{2}+c_{1} x} \\ y \relax (x ) = -\sqrt {x^{2}+c_{1} x} \\ y \relax (x ) = -\frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 c_{1}\right )}}{3 x} \\ y \relax (x ) = \frac {\sqrt {3}\, \sqrt {x \left (-x^{3}+3 c_{1}\right )}}{3 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.524 (sec). Leaf size: 97
DSolve[4 x^2 y[x]^2(y'[x])^2 ==(x^2+y[x]^2)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x} \sqrt {x+c_1} \\ y(x)\to \sqrt {x} \sqrt {x+c_1} \\ y(x)\to -\frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ y(x)\to \frac {\sqrt {-x^3+3 c_1}}{\sqrt {3} \sqrt {x}} \\ \end{align*}