75.16.64 problem 537

Internal problem ID [17037]
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 : 537
Date solved : Tuesday, January 28, 2025 at 09:47:18 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=x*exp(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 50

DSolve[D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

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