8.4.2 problem 2

Internal problem ID [705]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.5. Linear first order equations. Page 56
Problem number : 2
Date solved : Monday, January 27, 2025 at 02:58:37 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 11

dsolve([-2*y(x)+diff(y(x),x) = 3*exp(2*x),y(0) = 0],y(x), singsol=all)
 

\[ y = 3 \,{\mathrm e}^{2 x} x \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 13

DSolve[{-2*y[x]+D[y[x],x] == 3*Exp[2*x],y[0]==0},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3 e^{2 x} x \]