29.31.10 problem 909

Internal problem ID [5489]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 909
Date solved : Monday, January 27, 2025 at 11:28:46 AM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x)^2-5*x*y(x)*diff(y(x),x)+6*y(x)^2 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= c_{1} x^{3} \\ y \left (x \right ) &= c_{1} x^{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.045 (sec). Leaf size: 26

DSolve[x^2 (D[y[x],x])^2-5 x y[x] D[y[x],x]+6 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x^2 \\ y(x)\to c_1 x^3 \\ y(x)\to 0 \\ \end{align*}