83.43.14 problem Ex 15 page 15

Internal problem ID [19451]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 15 page 15
Date solved : Monday, March 31, 2025 at 07:15:08 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.011 (sec). Leaf size: 21

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

\[ y = \arctan \left (\frac {{\mathrm e}^{-x^{2}} c_1}{2}+\frac {x^{2}}{2}-\frac {1}{2}\right ) \]

✓ Mathematica. Time used: 18.565 (sec). Leaf size: 105

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

\begin{align*} y(x)\to \arctan \left (\frac {1}{2} \left (x^2-8 c_1 e^{-x^2}-1\right )\right ) \\ y(x)\to -\arctan \left (-\frac {x^2}{2}+4 c_1 e^{-x^2}+\frac {1}{2}\right ) \\ y(x)\to -\frac {1}{2} \pi e^{x^2} \sqrt {e^{-2 x^2}} \\ y(x)\to \frac {1}{2} \pi e^{x^2} \sqrt {e^{-2 x^2}} \\ \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -x*(x**2*cos(y(x))**2 - sin(2*y(x))) + Derivative(y(x), x) cannot be solved by the factorable group method