29.1.6 problem 5

Internal problem ID [4613]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 5
Date solved : Monday, January 27, 2025 at 09:26:17 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=a \sin \left (b x +c \right )+k y \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 48

dsolve(diff(y(x),x) = a*sin(b*x+c)+k*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-a b \cos \left (b x +c \right )-a \sin \left (b x +c \right ) k +{\mathrm e}^{k x} c_{1} \left (b^{2}+k^{2}\right )}{b^{2}+k^{2}} \]

✓ Solution by Mathematica

Time used: 0.117 (sec). Leaf size: 43

DSolve[D[y[x],x]==a*Sin[b*x+c]+k*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {a (k \sin (b x+c)+b \cos (b x+c))}{b^2+k^2}+c_1 e^{k x} \]