76.2.9 problem 9

Internal problem ID [17345]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 10:01:55 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y = 3 t -6+{\mathrm e}^{-\frac {t}{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 37

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

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