67.4.11 problem Problem 2(j)[k]

Internal problem ID [14055]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number : Problem 2(j)[k]
Date solved : Tuesday, January 28, 2025 at 06:13:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 y^{\prime \prime }-4 y^{\prime }+y&=t^{2} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=-12\\ y^{\prime }\left (0\right )&=7 \end{align*}

✓ Solution by Maple

Time used: 7.500 (sec). Leaf size: 22

dsolve([4*diff(y(t),t$2)-4*diff(y(t),t)+y(t)=t^2,y(0) = -12, D(y)(0) = 7],y(t), singsol=all)
 

\[ y = t^{2}+8 t +24+{\mathrm e}^{\frac {t}{2}} \left (17 t -36\right ) \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 26

DSolve[{4*D[y[t],{t,2}]-4*D[y[t],t]+y[t]==t^2,{y[0]==-12,Derivative[1][y][0] ==7}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to t^2+8 t+e^{t/2} (17 t-36)+24 \]