76.2.35 problem 43

Internal problem ID [17371]
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 : 43
Date solved : Tuesday, January 28, 2025 at 10:03:21 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

\[ y = 3 t^{2}-12 t +24+{\mathrm e}^{-\frac {t}{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 39

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

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