68.6.22 problem 23

Internal problem ID [17332]
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 : 23
Date solved : Thursday, October 02, 2025 at 02:02:58 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 40

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

\begin{align*} y &= 0 \\ y &= \sqrt {-\cos \left (t^{2}\right ) c_1}\, \sec \left (t^{2}\right ) \\ y &= -\sqrt {-\cos \left (t^{2}\right ) c_1}\, \sec \left (t^{2}\right ) \\ \end{align*}

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 26

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

\begin{align*} y(t)&\to 0\\ y(t)&\to \frac {c_1}{\sqrt {\cos \left (t^2\right )}}\\ y(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.265 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = C_{1} \sqrt [4]{\frac {1}{\cos ^{2}{\left (t^{2} \right )}}} \]