74.6.38 problem 39

Internal problem ID [16061]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 39
Date solved : Tuesday, January 28, 2025 at 08:34:05 AM
CAS classification : [_exact, _rational, _Bernoulli]

\begin{align*} \frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime }&=0 \end{align*}

With initial conditions

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

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

Not solved