Internal problem ID [9338]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1004.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=a \cos \left (b x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(diff(y(x),x),x)+y(x)-a*cos(b*x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} -\frac {a \cos \left (b x \right )}{b^{2}-1} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 30
DSolve[-(a*Cos[b*x]) + y[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {a \cos (b x)}{b^2-1}+c_1 \cos (x)+c_2 \sin (x) \]