83.22.9 problem 9

Internal problem ID [19192]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (E) at page 63
Problem number : 9
Date solved : Monday, March 31, 2025 at 06:53:17 PM
CAS classification : [_quadrature]

\begin{align*} 2 {y^{\prime }}^{3}-\left (2 x +4 \sin \left (x \right )-\cos \left (x \right )\right ) {y^{\prime }}^{2}-\left (x \cos \left (x \right )-4 x \sin \left (x \right )+\sin \left (2 x \right )\right ) y^{\prime }+x \sin \left (2 x \right )&=0 \end{align*}

✓ Maple. Time used: 0.048 (sec). Leaf size: 29

ode:=2*diff(y(x),x)^3-(2*x+4*sin(x)-cos(x))*diff(y(x),x)^2-(x*cos(x)-4*x*sin(x)+sin(2*x))*diff(y(x),x)+x*sin(2*x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {x^{2}}{2}+c_1 \\ y &= -\frac {\sin \left (x \right )}{2}+c_1 \\ y &= -2 \cos \left (x \right )+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 39

ode=2*D[y[x],x]^3-(2*x+4*Sin[x]-Cos[x])*D[y[x],x]^2-(x*Cos[x]-4*x*Sin[x]+Sin[2*x])*D[y[x],x]+x*Sin[2*x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*sin(2*x) - (2*x + 4*sin(x) - cos(x))*Derivative(y(x), x)**2 - (-4*x*sin(x) + x*cos(x) + sin(2*x))*Derivative(y(x), x) + 2*Derivative(y(x), x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out