49.22.7 problem 1(g)

Internal problem ID [7753]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 5. Existence and uniqueness of solutions to first order equations. Page 198
Problem number : 1(g)
Date solved : Sunday, March 30, 2025 at 12:22:41 PM
CAS classification : [_exact]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 19

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

\[ \cos \left (y\right ) x^{2}+y \,{\mathrm e}^{2 x}+c_1 = 0 \]

✓ Mathematica. Time used: 0.423 (sec). Leaf size: 30

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

\[ \text {Solve}\left [2 \left (\frac {1}{2} x^2 \cos (y(x))+\frac {1}{2} e^{2 x} y(x)\right )=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out