72.6.13 problem 21

Internal problem ID [14738]
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
Date solved : Tuesday, January 28, 2025 at 07:13:15 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&=t^{2}+2 t +1+{\mathrm e}^{4 t} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 26

dsolve(diff(y(t),t)+2*y(t)=t^2+2*t+1+exp(4*t),y(t), singsol=all)
 

\[ y = \frac {t^{2}}{2}+\frac {t}{2}+\frac {1}{4}+\frac {{\mathrm e}^{4 t}}{6}+c_{1} {\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.561 (sec). Leaf size: 41

DSolve[D[y[t],t]+2*y[t]==t^2+2*t+1+Exp[4*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-2 t} \left (\int _1^te^{2 K[1]} \left ((K[1]+1)^2+e^{4 K[1]}\right )dK[1]+c_1\right ) \]