69.4.3 problem 48

Internal problem ID [17992]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 48
Date solved : Thursday, October 02, 2025 at 02:32:33 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 6

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

\[ y = \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 7

ode=D[y[x],x]*Sin[x]-y[x]*Cos[x]==0; 
ic={y[Pi/2]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \sin (x) \end{align*}

✓ Sympy. Time used: 0.143 (sec). Leaf size: 5

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

\[ y{\left (x \right )} = \sin {\left (x \right )} \]