83.8.30 problem 31

Internal problem ID [19085]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 31
Date solved : Monday, March 31, 2025 at 06:48:01 PM
CAS classification : [`x=_G(y,y')`]

\begin{align*} y-x y^{\prime }+x^{2}+1+x^{2} \sin \left (y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 21

ode:=y(x)-x*diff(y(x),x)+x^2+1+x^2*sin(y(x))*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ x +\frac {-y-1}{x}-\cos \left (y\right )+c_1 = 0 \]

✓ Mathematica. Time used: 0.137 (sec). Leaf size: 25

ode=y[x]-x*D[y[x],x]+(1+x^2)+x^2*Sin[y[x]]*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*sin(y(x))*Derivative(y(x), x) + x**2 - x*Derivative(y(x), x) + y(x) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out