10.1.12 problem 12

Internal problem ID [1109]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 12
Date solved : Monday, January 27, 2025 at 04:33:44 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

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

dsolve(y(t)+2*diff(y(t),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: 0.055 (sec). Leaf size: 25

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

\[ y(t)\to 3 t^2-12 t+c_1 e^{-t/2}+24 \]