29.31.6 problem 905

Internal problem ID [5485]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 905
Date solved : Monday, January 27, 2025 at 11:27:23 AM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x)^2+3*x*diff(y(x),x)*y(x)+2*y(x)^2 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {c_{1}}{x} \\ y \left (x \right ) &= \frac {c_{1}}{x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 26

DSolve[x^2 (D[y[x],x])^2+3 x y[x] D[y[x],x]+2 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1}{x^2} \\ y(x)\to \frac {c_1}{x} \\ y(x)\to 0 \\ \end{align*}