15.8.48 problem 51

Internal problem ID [3051]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 51
Date solved : Monday, January 27, 2025 at 07:12:39 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 17

dsolve([diff(y(x),x)+2*y(x)=3*exp(2*x),y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 23

DSolve[{D[y[x],x]+2*y[x]==3*Exp[2*x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-2 x} \left (3 e^{4 x}+1\right ) \]