Internal problem ID [4541]
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`]]
\[ \boxed {y^{\prime }+a y=b \sin \left (k x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(diff(y(x),x)+a*y(x)=b*sin(k*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-a x} c_{1} -\frac {b \left (k \cos \left (k x \right )-\sin \left (k x \right ) a \right )}{a^{2}+k^{2}} \]
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 40
DSolve[y'[x]+a*y[x]==b*Sin[k*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {b (a \sin (k x)-k \cos (k x))}{a^2+k^2}+c_1 e^{-a x} \]