13.2.15 problem 16

Internal problem ID [2313]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 16
Date solved : Monday, January 27, 2025 at 05:45:25 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 (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 15

dsolve([4*t*y(t)+(t^2+1)*diff(y(t),t) = t,y(0) = 0],y(t), singsol=all)
 

\[ y = \frac {1}{4}-\frac {1}{4 \left (t^{2}+1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 24

DSolve[{4*t*y[t]+(t^2+1)*D[y[t],t]== t,y[0]==0},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {t^2 \left (t^2+2\right )}{4 \left (t^2+1\right )^2} \]