83.4.7 problem 2 (b)

Internal problem ID [21934]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. V at page 42
Problem number : 2 (b)
Date solved : Thursday, October 02, 2025 at 08:15:48 PM
CAS classification : [_exact]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.121 (sec). Leaf size: 28

ode:=2*x*sin(y(x))+2*x+3*y(x)*cos(x)+(x^2*cos(y(x))+3*sin(x))*diff(y(x),x) = 0; 
ic:=[y(1/2*Pi) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (4 x^{2} \sin \left (\textit {\_Z} \right )-\pi ^{2}+12 \textit {\_Z} \sin \left (x \right )+4 x^{2}\right ) \]

✓ Mathematica. Time used: 0.225 (sec). Leaf size: 28

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

\[ \text {Solve}\left [x^2 \sin (y(x))+x^2+3 y(x) \sin (x)=\frac {\pi ^2}{4},y(x)\right ] \]

✗ Sympy

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

Timed Out