Internal problem ID [2997]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 249.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-a +y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 12
dsolve(x^2*diff(y(x),x) = a-y(x),y(x), singsol=all)
\[ y \relax (x ) = a +{\mathrm e}^{\frac {1}{x}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 20
DSolve[x^2 y'[x]==a-y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a+c_1 e^{\frac {1}{x}} \\ y(x)\to a \\ \end{align*}