29.29.4 problem 826

Internal problem ID [5409]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 29
Problem number : 826
Date solved : Monday, January 27, 2025 at 11:21:16 AM
CAS classification : [_separable]

\begin{align*} {y^{\prime }}^{2}-x y \left (x^{2}+y^{2}\right ) y^{\prime }+x^{4} y^{4}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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 \left (x \right ) &= \frac {1}{\sqrt {-x^{2}+c_{1}}} \\ y \left (x \right ) &= -\frac {1}{\sqrt {-x^{2}+c_{1}}} \\ y \left (x \right ) &= c_{1} {\mathrm e}^{\frac {x^{4}}{4}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.202 (sec). Leaf size: 60

DSolve[(D[y[x],x])^2-x*y[x]*(x^2+y[x]^2)*D[y[x],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*}