74.5.49 problem 56

Internal problem ID [16013]
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 : 56
Date solved : Tuesday, January 28, 2025 at 08:26:30 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 33

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

\[ y(t)\to e^{3 t} \left (\int _1^t27 e^{-3 K[1]} K[1]^2dK[1]+c_1\right ) \]