Internal problem ID [1893]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+y^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (3) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 14
dsolve([x^2*diff(y(x),x)+y(x)^2=0,y(3) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {3 x}{4 x -3} \]
✓ Solution by Mathematica
Time used: 0.131 (sec). Leaf size: 15
DSolve[{x^2*y'[x]+y[x]^2==0,y[3]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 x}{4 x-3} \\ \end{align*}