68.6.23 problem 24

Internal problem ID [17333]
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 : 24
Date solved : Thursday, October 02, 2025 at 02:02:58 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.010 (sec). Leaf size: 20

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

\[ y = \frac {\operatorname {RootOf}\left (t^{3}+\textit {\_Z} \cos \left (\textit {\_Z} \right )+c_1 t \right )}{t} \]

✓ Mathematica. Time used: 0.183 (sec). Leaf size: 89

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

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

✗ Sympy

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

Timed Out