60.1.438 problem 440

Internal problem ID [10452]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 440
Date solved : Monday, January 27, 2025 at 07:45:49 PM
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*y(x)*diff(y(x),x)-5*y(x)^2 = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 24

DSolve[-5*y[x]^2 + 4*x*y[x]*D[y[x],x] + x^2*D[y[x],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*}