74.6.36 problem 37

Internal problem ID [15988]
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 : Monday, March 31, 2025 at 02:21:31 PM
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*}

✓ Maple. Time used: 0.347 (sec). Leaf size: 25

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

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

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

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

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

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((2*t*y(t) + 1)*Derivative(y(t), t) + y(t)**2 - 2*sin(2*t),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out