82.28.3 problem Ex. 4

Internal problem ID [18882]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 75
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:33:20 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=3 \,{\mathrm e}^{\frac {5 x}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=3*exp(5/2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {4 \,{\mathrm e}^{\frac {5 x}{2}}}{3}+\left (c_{1} x +c_{2} \right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 28

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==3*Exp[5/2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {4}{3} e^{5 x/2}+e^x (c_2 x+c_1) \]