68.6.25 problem 26

Internal problem ID [17335]
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 : 26
Date solved : Thursday, October 02, 2025 at 02:04:43 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.038 (sec). Leaf size: 19

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

\[ \cos \left (t^{2}\right ) y+t^{2} \sin \left (y\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.229 (sec). Leaf size: 76

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

\[ \text {Solve}\left [\int _1^{y(t)}\left (\cos (K[2]) t^2+\cos \left (t^2\right )-\int _1^t-2 K[1] \left (\sin \left (K[1]^2\right )-\cos (K[2])\right )dK[1]\right )dK[2]+\int _1^t-2 K[1] \left (\sin \left (K[1]^2\right ) y(t)-\sin (y(t))\right )dK[1]=c_1,y(t)\right ] \]

✗ Sympy

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

Timed Out