39.2.2 problem Problem 11.45

Internal problem ID [6519]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. Supplementary Problems. page 101
Problem number : Problem 11.45
Date solved : Monday, January 27, 2025 at 02:11:19 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=4 \,{\mathrm e}^{2 x} \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)=4*exp(2*x),y(x), singsol=all)
 

\[ y = 4 \,{\mathrm e}^{2 x}+\left (c_1 x +c_2 \right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 21

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==4*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (4 e^x+c_2 x+c_1\right ) \]