Internal problem ID [7592]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+f \relax (x ) y-g \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x) + f(x)*y(x) - g(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (\int g \relax (x ) {\mathrm e}^{\int f \relax (x )d x}d x +c_{1}\right ) {\mathrm e}^{\int -f \relax (x )d x} \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 51
DSolve[y'[x] + f[x]*y[x] - g[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (\int _1^x-f(K[1])dK[1]\right ) \left (\int _1^x\exp \left (-\int _1^{K[2]}-f(K[1])dK[1]\right ) g(K[2])dK[2]+c_1\right ) \\ \end{align*}