Internal problem ID [15338]
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. Superposition principle. Exercises page 137
Problem number: 569.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y=10 \sin \left (x \right )+17 \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+5*y(x)=10*sin(x)+17*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{x}+4\right ) \cos \left (2 x \right )+{\mathrm e}^{x} \sin \left (2 x \right ) c_{2} +\cos \left (x \right )+2 \sin \left (x \right )+\sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.538 (sec). Leaf size: 37
DSolve[y''[x]-2*y'[x]+5*y[x]==10*Sin[x]+17*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cos (x)+\left (4+c_2 e^x\right ) \cos (2 x)+2 \sin (x) \left (\cos (x)+c_1 e^x \cos (x)+1\right ) \]