60.1.446 problem 449

Internal problem ID [10460]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 449
Date solved : Monday, January 27, 2025 at 07:46:08 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

\begin{align*} y &= \frac {c_{1}}{a -x} \\ y &= \frac {c_{1}}{a +x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 32

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

\begin{align*} y(x)\to \frac {c_1}{a-x} \\ y(x)\to \frac {c_1}{a+x} \\ y(x)\to 0 \\ \end{align*}