29.34.8 problem 1004

Internal problem ID [5579]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 34
Problem number : 1004
Date solved : Monday, January 27, 2025 at 12:11:19 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

\begin{align*} 4 x^{2} y^{2} {y^{\prime }}^{2}&=\left (x^{2}+y^{2}\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.008 (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: 0.541 (sec). Leaf size: 97

DSolve[4 x^2 y[x]^2(D[y[x],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*}