79.5.1 problem (a)

Internal problem ID [21093]
Book : Ordinary Differential Equations. By Wolfgang Walter. Graduate texts in Mathematics. Springer. NY. QA372.W224 1998
Section : Chapter 1. First order equations: Some integrable cases. Excercises IX at page 45
Problem number : (a)
Date solved : Thursday, October 02, 2025 at 07:07:28 PM
CAS classification : [_exact]

\begin{align*} \cos \left (x +y^{2}\right )+3 y+\left (2 y \cos \left (x +y^{2}\right )+3 x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 41

ode:=cos(x+y(x)^2)+3*y(x)+(2*y(x)*cos(x+y(x)^2)+3*x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-c_1 -\sin \left (\operatorname {RootOf}\left (-9 x^{2} \textit {\_Z} +9 x^{3}+\sin \left (\textit {\_Z} \right )^{2}+2 c_1 \sin \left (\textit {\_Z} \right )+c_1^{2}\right )\right )}{3 x} \]

✓ Mathematica. Time used: 0.183 (sec). Leaf size: 28

ode=(Cos[x+y[x]^2]+3*y[x])+(2*y[x]*Cos[x+y[x]^2]+3*x)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [3 x y(x)+\sin (x) \cos \left (y(x)^2\right )+\cos (x) \sin \left (y(x)^2\right )=c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3*x + 2*y(x)*cos(x + y(x)**2))*Derivative(y(x), x) + 3*y(x) + cos(x + y(x)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out