82.33.13 problem Ex. 13

Internal problem ID [18906]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 13
Date solved : Tuesday, January 28, 2025 at 12:34:08 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

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

\[ y \left (x \right ) = \frac {\left (2 x^{2}-4 x +3\right ) {\mathrm e}^{3 x}}{8}+{\mathrm e}^{x} \left (c_{1} x +c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 36

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

\[ y(x)\to \frac {1}{8} e^{3 x} \left (2 x^2-4 x+3\right )+e^x (c_2 x+c_1) \]