Internal problem ID [12724]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page
136
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+3 y={\mathrm e}^{-2 t}+t^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(t),t)= -3*y(t)+exp(-2*t)+t^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {t^{2}}{3}-\frac {2 t}{9}+\frac {2}{27}+{\mathrm e}^{-2 t}+c_{1} {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.147 (sec). Leaf size: 33
DSolve[y'[t]==-3*y[t]+Exp[-2*t]+t^2,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{27} \left (9 t^2-6 t+2\right )+e^{-2 t}+c_1 e^{-3 t} \]