72.6.12 problem 20

Internal problem ID [14737]
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 : 20
Date solved : Tuesday, January 28, 2025 at 07:13:13 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&=3 t^{2}+2 t -1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(diff(y(t),t)+2*y(t)=3*t^2+2*t-1,y(t), singsol=all)
 

\[ y = \frac {3 t^{2}}{2}-\frac {t}{2}-\frac {1}{4}+c_{1} {\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.123 (sec). Leaf size: 40

DSolve[D[y[t],t]+2*y[t]==3*t^2+2*t-1,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-2 t} \left (\int _1^te^{2 K[1]} \left (3 K[1]^2+2 K[1]-1\right )dK[1]+c_1\right ) \]