75.17.11 problem 561

Internal problem ID [17060]
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 : 561
Date solved : Tuesday, January 28, 2025 at 09:48:06 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.216 (sec). Leaf size: 61

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

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