68.6.27 problem 28

Internal problem ID [17337]
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 : 28
Date solved : Thursday, October 02, 2025 at 02:05:45 PM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 63

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

\begin{align*} y &= \frac {-\sin \left (t^{2}\right )+\sqrt {\sin \left (t^{2}\right )^{2}-4 t^{2} c_1}}{2 t} \\ y &= \frac {-\sin \left (t^{2}\right )-\sqrt {\sin \left (t^{2}\right )^{2}-4 t^{2} c_1}}{2 t} \\ \end{align*}

✓ Mathematica. Time used: 0.429 (sec). Leaf size: 94

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

\begin{align*} y(t)&\to -\frac {\sin \left (t^2\right )+\sqrt {\frac {1}{t^2}} t \sqrt {\sin ^2\left (t^2\right )+4 c_1 t^2}}{2 t}\\ y(t)&\to \frac {-\sin \left (t^2\right )+\sqrt {\frac {1}{t^2}} t \sqrt {\sin ^2\left (t^2\right )+4 c_1 t^2}}{2 t}\\ y(t)&\to 0 \end{align*}

✗ Sympy

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

Timed Out