Internal problem ID [12637]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-\frac {3 y}{\left (-5+x \right ) \left (x +3\right )}={\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(diff(y(x),x)=3*y(x)/( (x-5)*(x+3))+exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\int \frac {{\mathrm e}^{-x} \left (x +3\right )^{\frac {3}{8}}}{\left (x -5\right )^{\frac {3}{8}}}d x +c_{1} \right ) \left (x -5\right )^{\frac {3}{8}}}{\left (x +3\right )^{\frac {3}{8}}} \]
✓ Solution by Mathematica
Time used: 15.323 (sec). Leaf size: 57
DSolve[y'[x]==3*y[x]/( (x-5)*(x+3))+Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {(5-x)^{3/8} \left (\int _1^x\frac {e^{-K[1]} (K[1]+3)^{3/8}}{(5-K[1])^{3/8}}dK[1]+c_1\right )}{(x+3)^{3/8}} \]