83.48.6 problem Ex 6 page 100

Internal problem ID [19527]
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 VII. Exact differential equations.
Problem number : Ex 6 page 100
Date solved : Monday, March 31, 2025 at 07:29:19 PM
CAS classification : [[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 32

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

\[ y = -\arcsin \left (\frac {2 c_2 \,x^{{3}/{2}}+\left (3 \ln \left (x \right )-3\right ) \sqrt {x}-2 c_1}{3 \sqrt {x}}\right ) \]

✓ Mathematica. Time used: 57.887 (sec). Leaf size: 59

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

\begin{align*} y(x)\to \arcsin \left (-\log (x)+\frac {2 c_1}{3 \sqrt {x}}+\frac {c_2 x}{2}+1\right ) \\ y(x)\to \arcsin \left (-\log (x)+\frac {2 c_1}{3 \sqrt {x}}+\frac {c_2 x}{2}+1\right ) \\ \end{align*}

✗ Sympy

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

ZeroDivisionError : polynomial division