Internal problem ID [12871]
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: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }=3 t +2} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)+2*diff(y(t),t)=3*t+2,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {3 t^{2}}{4}+\frac {{\mathrm e}^{-2 t}}{8}+\frac {t}{4}-\frac {1}{8} \]
✓ Solution by Mathematica
Time used: 0.131 (sec). Leaf size: 24
DSolve[{y''[t]+2*y'[t]==3*t+2,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} \left (6 t^2+2 t+e^{-2 t}-1\right ) \]