18.1.25 problem Problem 14.30 (a)

Internal problem ID [3481]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.30 (a)
Date solved : Sunday, March 30, 2025 at 01:44:17 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

With initial conditions

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

✓ Maple. Time used: 0.007 (sec). Leaf size: 5

ode:=(2*sin(y(x))-x)*diff(y(x),x) = tan(y(x)); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 6

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

\[ y(x)\to 0 \]

✗ Sympy

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