Internal problem ID [7584]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+a y-b \sin \left (x c \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve(diff(y(x),x) + a*y(x) - b*sin(c*x)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-a x} c_{1}-\frac {b \left (c \cos \left (c x \right )-\sin \left (c x \right ) a \right )}{a^{2}+c^{2}} \]
✓ Solution by Mathematica
Time used: 0.135 (sec). Leaf size: 40
DSolve[y'[x] + a*y[x] - b*Sin[c*x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {b (a \sin (c x)-c \cos (c x))}{a^2+c^2}+c_1 e^{-a x} \\ \end{align*}