76.19.4 problem 4

Internal problem ID [17728]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 5. The Laplace transform. Section 5.4 (Solving differential equations with Laplace transform). Problems at page 327
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 11:01:55 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 )&=1\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 9.519 (sec). Leaf size: 13

dsolve([diff(y(t),t$2)-4*diff(y(t),t)+4*y(t)=0,y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
 

\[ y = -\left (t -1\right ) {\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 22

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

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