74.5.45 problem 52

Internal problem ID [16009]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 52
Date solved : Tuesday, January 28, 2025 at 08:26:23 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+3 y&=27 t^{2}+9 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(t),t)+3*y(t)=27*t^2+9,y(t), singsol=all)
 

\[ y = 9 t^{2}-6 t +5+{\mathrm e}^{-3 t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.204 (sec). Leaf size: 37

DSolve[D[y[t],t]+3*y[t]==27*t^2+9,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-3 t} \left (\int _1^t9 e^{3 K[1]} \left (3 K[1]^2+1\right )dK[1]+c_1\right ) \]