Internal problem ID [2793]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 2
Problem number: 38.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-f \relax (x )-g \relax (x ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 24
dsolve(diff(y(x),x) = f(x)+g(x)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \left (\int f \relax (x ) {\mathrm e}^{-\left (\int g \relax (x )d x \right )}d x +c_{1}\right ) {\mathrm e}^{\int g \relax (x )d x} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 47
DSolve[y'[x]==f[x] + g[x] y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (\int _1^xg(K[1])dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}g(K[1])dK[1]\right ) f(K[2])dK[2]+c_1\right ) \\ \end{align*}