14.1.16 problem 16

Internal problem ID [2487]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.2. Linear equations. Excercises page 9
Problem number : 16
Date solved : Monday, January 27, 2025 at 05:54:06 AM
CAS classification : [_separable]

\begin{align*} 4 y t +\left (t^{2}+1\right ) y^{\prime }&=t \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&={\frac {1}{4}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 5

dsolve([(1+t^2)*diff(y(t),t)+4*t*y(t)=t,y(1) = 1/4],y(t), singsol=all)
 

\[ y = {\frac {1}{4}} \]

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 8

DSolve[{(1+t^2)*D[y[t],t]+4*t*y[t]==t,{y[1]==1/4}},y[t],t,IncludeSingularSolutions -> True]
 

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