Internal problem ID [4235]
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]
\[ \boxed {4 x^{2} y^{2} {y^{\prime }}^{2}-\left (y^{2}+x^{2}\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 69
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 \left (x \right ) &= \sqrt {\left (x +c_{1} \right ) x} \\ y \left (x \right ) &= -\sqrt {\left (x +c_{1} \right ) x} \\ y \left (x \right ) &= -\frac {\sqrt {3}\, \sqrt {-x \left (x^{3}-3 c_{1} \right )}}{3 x} \\ y \left (x \right ) &= \frac {\sqrt {3}\, \sqrt {-x \left (x^{3}-3 c_{1} \right )}}{3 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.526 (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*}