Internal problem ID [5100]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.3 SECOND ORDER ODE. Page
147
Problem number: Example 3.22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-3 y^{\prime }+2 y-x \,{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=x*exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = \left (c_{1} {\mathrm e}^{x}+\frac {{\mathrm e}^{x} x^{2}}{2}-x \,{\mathrm e}^{x}+{\mathrm e}^{x}+c_{2}\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 33
DSolve[y''[x]-3*y'[x]+2*y[x]==x*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^x \left (e^x \left (x^2-2 x+2+2 c_2\right )+2 c_1\right ) \\ \end{align*}