37.2.1 problem 10.3.2

Internal problem ID [6398]
Book : Basic Training in Mathematics. By R. Shankar. Plenum Press. NY. 1995
Section : Chapter 10, Differential equations. Section 10.3, ODEs with variable Coefficients. First order. page 315
Problem number : 10.3.2
Date solved : Monday, January 27, 2025 at 02:00:29 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 11

dsolve(diff(y(x),x)-y(x)=exp(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 15

DSolve[D[y[x],x]-y[x]==Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

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