74.11.50 problem 62 (a)

Internal problem ID [16300]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number : 62 (a)
Date solved : Tuesday, January 28, 2025 at 09:02:06 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-4 y&=t^{2} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(t),t)-4*y(t)=t^2,y(t), singsol=all)
 

\[ y = -\frac {t^{2}}{4}-\frac {t}{8}-\frac {1}{32}+{\mathrm e}^{4 t} c_{1} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 32

DSolve[D[y[t],t]-4*y[t]==t^2,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{4 t} \left (\int _1^te^{-4 K[1]} K[1]^2dK[1]+c_1\right ) \]