72.16.32 problem 33

Internal problem ID [14928]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number : 33
Date solved : Tuesday, January 28, 2025 at 07:20:56 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }&=3 t +2 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 20

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

\[ y = \frac {3 t^{2}}{8}+\frac {5 \,{\mathrm e}^{-4 t}}{64}+\frac {5 t}{16}-\frac {5}{64} \]

✓ Solution by Mathematica

Time used: 4.520 (sec). Leaf size: 124

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

\[ y(t)\to \int _1^te^{-4 K[2]} \left (\int _1^{K[2]}e^{4 K[1]} (3 K[1]+2)dK[1]-\int _1^0e^{4 K[1]} (3 K[1]+2)dK[1]\right )dK[2]-\int _1^0e^{-4 K[2]} \left (\int _1^{K[2]}e^{4 K[1]} (3 K[1]+2)dK[1]-\int _1^0e^{4 K[1]} (3 K[1]+2)dK[1]\right )dK[2] \]