74.3.20 problem 15

Internal problem ID [15880]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 08:17:06 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 14

dsolve([t*diff(y(t),t)+y(t)=t^3,y(1) = 0],y(t), singsol=all)
 

\[ y = \frac {t^{4}-1}{4 t} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 17

DSolve[{t*D[y[t],t]+y[t]==t^3,{y[1]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {t^4-1}{4 t} \]