Internal problem ID [7583]
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`]]
\[ \boxed {y^{\prime }+a y-b \sin \left (c x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x) + a*y(x) - b*sin(c*x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-a x} c_{1} +\frac {b \left (\sin \left (c x \right ) a -c \cos \left (c x \right )\right )}{a^{2}+c^{2}} \]
✓ Solution by Mathematica
Time used: 0.087 (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*}