Internal problem ID [15496]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 18.3. Finding periodic solutions of linear
differential equations. Exercises page 187
Problem number: 759.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y=\cos \left (\pi x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 41
dsolve(diff(y(x),x$2)-4*y(x)=cos(Pi*x),y(x), singsol=all)
\[ y = \frac {c_{1} \left (\pi ^{2}+4\right ) {\mathrm e}^{-2 x}+c_{2} \left (\pi ^{2}+4\right ) {\mathrm e}^{2 x}-\cos \left (\pi x \right )}{\pi ^{2}+4} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 35
DSolve[y''[x]-4*y[x]==Cos[Pi*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\cos (\pi x)}{4+\pi ^2}+c_1 e^{2 x}+c_2 e^{-2 x} \]