Internal problem ID [3268]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-k y=a \cos \left (b x +c \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(diff(y(x),x) = a*cos(b*x+c)+k*y(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{k x} c_{1} +\frac {a \left (b \sin \left (x b +c \right )-\cos \left (x b +c \right ) k \right )}{b^{2}+k^{2}} \]
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 43
DSolve[y'[x]==a*Cos[b*x+c]+k*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {a (b \sin (b x+c)-k \cos (b x+c))}{b^2+k^2}+c_1 e^{k x} \]