Internal problem ID [4033]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.20, page 103.
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 (k x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 38
dsolve(diff(y(x),x)+a*y(x)=b*sin(k*x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-a x}-\frac {b \left (k \cos \left (k x \right )-\sin \left (k x \right ) a \right )}{a^{2}+k^{2}} \]
✓ Solution by Mathematica
Time used: 0.085 (sec). Leaf size: 40
DSolve[y'[x]+a*y[x]==b*Sin[k*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {b (a \sin (k x)-k \cos (k x))}{a^2+k^2}+c_1 e^{-a x} \\ \end{align*}