72.16.22 problem 23

Internal problem ID [14918]
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 : 23
Date solved : Tuesday, January 28, 2025 at 07:20:20 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+10 y&=10 \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: 0.026 (sec). Leaf size: 25

dsolve([diff(y(t),t$2)+2*diff(y(t),t)+10*y(t)=10,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
 

\[ y = 1+\frac {\left (-\sin \left (3 t \right )-3 \cos \left (3 t \right )\right ) {\mathrm e}^{-t}}{3} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 32

DSolve[{D[y[t],{t,2}]+2*D[y[t],t]+10*y[t]==10,{y[0]==0,Derivative[1][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} e^{-t} \left (3 e^t-\sin (3 t)-3 \cos (3 t)\right ) \]