78.23.2 problem 3 (b)

Internal problem ID [18453]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 9. Laplace transforms. Section 50. Applications to differential equations. Problems at page 462
Problem number : 3 (b)
Date solved : Tuesday, January 28, 2025 at 11:50:19 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.175 (sec). Leaf size: 11

dsolve([diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=0,y(0) = 0, D(y)(0) = 3],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 13

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==0,{y[0]==0,Derivative[1][y][0] == 3}},y[x],x,IncludeSingularSolutions -> True]
 

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