14.2.7 problem 7

Internal problem ID [2495]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.4 separable equations. Excercises page 24
Problem number : 7
Date solved : Monday, January 27, 2025 at 05:54:26 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (2\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 20

dsolve([diff(y(t),t)=2*t/(y(t)+t^2*y(t)),y(2) = 3],y(t), singsol=all)
 

\[ y = \sqrt {9-2 \ln \left (5\right )+2 \ln \left (t^{2}+1\right )} \]

✓ Solution by Mathematica

Time used: 0.111 (sec). Leaf size: 23

DSolve[{D[y[t],t]==2*t/( y[t]+t^2*y[t]),{y[2]==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \sqrt {2 \log \left (t^2+1\right )+9-2 \log (5)} \]