29.31.8 problem 907

Internal problem ID [5487]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 907
Date solved : Monday, January 27, 2025 at 11:28:41 AM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(x^2*diff(y(x),x)^2+4*x*diff(y(x),x)*y(x)-5*y(x)^2 = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= c_{1} x \\ y \left (x \right ) &= \frac {c_{1}}{x^{5}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 24

DSolve[x^2 (D[y[x],x])^2+4 x y[x] D[y[x],x]-5 y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1}{x^5} \\ y(x)\to c_1 x \\ y(x)\to 0 \\ \end{align*}