74.6.50 problem 57

Internal problem ID [15994]
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 : 57
Date solved : Thursday, March 13, 2025 at 07:08:47 AM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.056 (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: 0.014 (sec). Leaf size: 43

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

\[ \text {Solve}\left [\left \{y''(x) (\cos (t y(t))-t y(t) \sin (t y(t)))+y(t)^2 (-\sin (t y(t)))+2 t=0\right \},\{y(t)\}\right ] \]

✗ 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