29.1.5 problem 4

Internal problem ID [4612]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 4
Date solved : Monday, January 27, 2025 at 09:26:15 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 47

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

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

✓ Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 43

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

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