60.3.4 problem 1004

Internal problem ID [11014]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1004
Date solved : Monday, January 27, 2025 at 10:41:31 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y-a \cos \left (b x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(diff(y(x),x),x)+y(x)-a*cos(b*x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 30

DSolve[-(a*Cos[b*x]) + y[x] + D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {a \cos (b x)}{b^2-1}+c_1 \cos (x)+c_2 \sin (x) \]