39.1.11 problem Problem 11.13

Internal problem ID [6516]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. page 95
Problem number : Problem 11.13
Date solved : Monday, January 27, 2025 at 02:11:14 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-5 y&=3 \,{\mathrm e}^{x}-2 x +1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(y(x),x)-5*y(x)=3*exp(x)-2*x+1,y(x), singsol=all)
 

\[ y = \frac {2 x}{5}-\frac {3}{25}-\frac {3 \,{\mathrm e}^{x}}{4}+{\mathrm e}^{5 x} c_1 \]

✓ Solution by Mathematica

Time used: 0.152 (sec). Leaf size: 29

DSolve[D[y[x],x]-5*y[x]==3*Exp[x]-2*x+1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 x}{5}-\frac {3 e^x}{4}+c_1 e^{5 x}-\frac {3}{25} \]