32.8.24 problem Exercise 21.32, page 231

Internal problem ID [5973]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined Coefficients
Problem number : Exercise 21.32, page 231
Date solved : Monday, January 27, 2025 at 01:29:38 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&={\mathrm e}^{x} \left (2 x -3\right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 13

dsolve([diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=exp(x)*(2*x-3),y(0) = 1, D(y)(0) = 3],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 35

DSolve[{D[y[x],{x,2}]-5*D[y[x],x]-6*y[x]==Exp[x]*(2*x-3),{y[0]==1,Derivative[1][y][0] ==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{175} e^{-x} \left (-7 e^{2 x} (5 x-9)+87 e^{7 x}+25\right ) \]