75.16.62 problem 535

Internal problem ID [17035]
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. Trial and error method. Exercises page 132
Problem number : 535
Date solved : Tuesday, January 28, 2025 at 09:47:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+5 y&=10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=10*exp(-2*x)*cos(x),y(x), singsol=all)
 

\[ y = \left (\left (c_{2} +5 x \right ) \sin \left (x \right )+\cos \left (x \right ) c_{1} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 45

DSolve[D[y[x],{x,2}]+4*D[y[x],x]+5*y[x]==10*Exp[-2*x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (\sin (x) \int _1^x10 \cos ^2(K[1])dK[1]+5 \cos ^3(x)+c_2 \cos (x)+c_1 \sin (x)\right ) \]