72.2.6 problem 6

Internal problem ID [14641]
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 1.3 page 47
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 06:45:54 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

dsolve(diff(y(t),t)=y(t)+t+1,y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 30

DSolve[D[y[t],t]==y[t]+t+1,y[t],t,IncludeSingularSolutions -> True]
 

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