Internal problem ID [13193]
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: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y=t^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve([diff(y(t),t$2)+3*diff(y(t),t)+2*y(t)=t^2,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {7}{4}-\frac {3 t}{2}+\frac {t^{2}}{2}+\frac {{\mathrm e}^{-2 t}}{4}-2 \,{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 37
DSolve[{y''[t]+3*y'[t]+2*y[t]==t^2,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^{-2 t} \left (e^{2 t} \left (2 t^2-6 t+7\right )-8 e^t+1\right ) \]