71.14.1 problem 7

Internal problem ID [14535]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.3, page 255
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 06:43:05 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-2 y&=6 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 8.851 (sec). Leaf size: 15

dsolve([diff(y(x),x)-2*y(x)=6,y(0) = 2],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 14

DSolve[{D[y[x],x]-2*y[x]==6,{y[0]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 5 e^{2 x}-3 \]