12.7.2 problem 2(a)

Internal problem ID [1712]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Integrating factors. Section 2.6 Page 91
Problem number : 2(a)
Date solved : Monday, January 27, 2025 at 05:32:08 AM
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: 0.107 (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*}