Internal problem ID [13002]
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. Exercises section 1.8 page 121
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }+2 y=t^{2}+2 t +1+{\mathrm e}^{4 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(t),t)+2*y(t)=t^2+2*t+1+exp(4*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {t^{2}}{2}+\frac {t}{2}+\frac {1}{4}+\frac {{\mathrm e}^{4 t}}{6}+{\mathrm e}^{-2 t} c_{1} \]
✓ Solution by Mathematica
Time used: 0.557 (sec). Leaf size: 35
DSolve[y'[t]+2*y[t]==t^2+2*t+1+Exp[4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{12} \left (6 t^2+6 t+2 e^{4 t}+3\right )+c_1 e^{-2 t} \]