85.26.3 problem 3

Internal problem ID [22591]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. C Exercises at page 57
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:53:47 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 96

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

\begin{align*} y &= {\mathrm e}^{\frac {x^{2}}{2}} \sqrt {-4 \,{\mathrm e}^{-x^{2}} \tan \left (\frac {x}{2}\right )^{2}+{\mathrm e}^{-\frac {x^{2}}{2}} c_1 \sec \left (\frac {x}{2}\right )^{4}}\, \cos \left (\frac {x}{2}\right )^{2} \\ y &= -{\mathrm e}^{\frac {x^{2}}{2}} \sqrt {-4 \,{\mathrm e}^{-x^{2}} \tan \left (\frac {x}{2}\right )^{2}+{\mathrm e}^{-\frac {x^{2}}{2}} c_1 \sec \left (\frac {x}{2}\right )^{4}}\, \cos \left (\frac {x}{2}\right )^{2} \\ \end{align*}

✓ Mathematica. Time used: 3.81 (sec). Leaf size: 57

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

\begin{align*} y(x)&\to -\sqrt {-\sin ^2(x)+c_1 e^{\frac {x^2}{2}}}\\ y(x)&\to \sqrt {-\sin ^2(x)+c_1 e^{\frac {x^2}{2}}} \end{align*}

✗ Sympy

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

Timed Out