Internal problem ID [3269]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 1
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-k y=a \sin \left (b x +c \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(diff(y(x),x) = a*sin(b*x+c)+k*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\cos \left (b x +c \right ) a b -\sin \left (b x +c \right ) a k +{\mathrm e}^{k x} c_{1} \left (b^{2}+k^{2}\right )}{b^{2}+k^{2}} \]
✓ Solution by Mathematica
Time used: 0.123 (sec). Leaf size: 43
DSolve[y'[x]==a*Sin[b*x+c]+k*y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {a (k \sin (b x+c)+b \cos (b x+c))}{b^2+k^2}+c_1 e^{k x} \]