Internal problem ID [15377]
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 15.3 Nonhomogeneous linear equations with
constant coefficients. Initial value problem. Exercises page 140
Problem number: 608.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y=\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=sin(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{2 x} \cos \left (x \right ) c_{1} +\frac {\cos \left (x \right )}{8}+\frac {\sin \left (x \right )}{8} \]
✓ Solution by Mathematica
Time used: 0.073 (sec). Leaf size: 36
DSolve[y''[x]-4*y'[x]+5*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{8} \left (\sin (x)+\cos (x)+8 c_2 e^{2 x} \cos (x)+8 c_1 e^{2 x} \sin (x)\right ) \]