74.6.36 problem 37

Internal problem ID [16059]
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 : 37
Date solved : Tuesday, January 28, 2025 at 08:32:44 AM
CAS classification : [_exact, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.404 (sec). Leaf size: 25

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

\[ y = \frac {-1+\sqrt {-4 \cos \left (2 t \right ) t +8 t +1}}{2 t} \]

✓ Solution by Mathematica

Time used: 2.014 (sec). Leaf size: 38

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

\[ y(t)\to \frac {\sqrt {8 t \int _0^t\sin (2 K[1])dK[1]+4 t+1}-1}{2 t} \]