75.17.13 problem 563

Internal problem ID [17062]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Superposition principle. Exercises page 137
Problem number : 563
Date solved : Tuesday, January 28, 2025 at 09:48:20 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 36

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=4*exp(-x)+17*sin(2*x),y(x), singsol=all)
 

\[ y = \left (\left (c_{1} +1\right ) \cos \left (2 x \right )+\sin \left (2 x \right ) c_{2} +1\right ) {\mathrm e}^{-x}-4 \cos \left (2 x \right )+\sin \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.346 (sec). Leaf size: 94

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+5*y[x]==4*Exp[-x]+17*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\cos (2 x) \int _1^x-\frac {1}{2} \sin (2 K[2]) \left (17 e^{K[2]} \sin (2 K[2])+4\right )dK[2]+\sin (2 x) \int _1^x\frac {1}{2} \cos (2 K[1]) \left (17 e^{K[1]} \sin (2 K[1])+4\right )dK[1]+c_2 \cos (2 x)+c_1 \sin (2 x)\right ) \]