29.9.9 problem 249

Internal problem ID [4849]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 249
Date solved : Monday, January 27, 2025 at 09:42:41 AM
CAS classification : [_separable]

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

✓ 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)
 

\[ y \left (x \right ) = a +c_{1} {\mathrm e}^{\frac {1}{x}} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 20

DSolve[x^2 D[y[x],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*}