29.31.3 problem 902

Internal problem ID [5482]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 902
Date solved : Monday, January 27, 2025 at 11:27:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.073 (sec). Leaf size: 32

dsolve(x^2*diff(y(x),x)^2-x*(x-2*y(x))*diff(y(x),x)+y(x)^2 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {x}{4} \\ y \left (x \right ) &= \frac {c_{1} \left (-c_{1} +x \right )}{x} \\ y \left (x \right ) &= -\frac {c_{1} \left (x +c_{1} \right )}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.211 (sec). Leaf size: 64

DSolve[x^2 (D[y[x],x])^2-x(x-2 y[x])D[y[x],x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^{-4 c_1}-2 i e^{-2 c_1} x}{4 x} \\ y(x)\to \frac {2 i e^{-2 c_1} x+e^{-4 c_1}}{4 x} \\ y(x)\to 0 \\ \end{align*}