40.2.3 problem 26

Internal problem ID [6581]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 4. Equations of first order and first degree (Variable separable). Supplemetary problems. Page 22
Problem number : 26
Date solved : Monday, January 27, 2025 at 02:14:06 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

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

\[ y = \frac {x}{c_1 x +1} \]

✓ Solution by Mathematica

Time used: 0.131 (sec). Leaf size: 21

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

\begin{align*} y(x)\to \frac {x}{1-c_1 x} \\ y(x)\to 0 \\ \end{align*}