49.1.7 problem HW 1 problem 13

Internal problem ID [9989]
Book : Selected problems from homeworks from different courses
Section : Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale college, Bloomington, Minnesota
Problem number : HW 1 problem 13
Date solved : Tuesday, September 30, 2025 at 06:45:48 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.13 (sec). Leaf size: 52

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (2 x K[2]+\sin (K[2])-\int _1^x2 K[2]dK[1]\right )dK[2]+\int _1^x\left (y(x)^2+\cos (K[1])\right )dK[1]=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out