75.6.23 problem 156

Internal problem ID [16708]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 156
Date solved : Monday, March 31, 2025 at 03:06:51 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.110 (sec). Leaf size: 6

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

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

✓ Mathematica. Time used: 0.853 (sec). Leaf size: 26

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

\[ y(x)\to \sec (x) \int _{\frac {\pi }{2}}^x-\sin (2 K[1])dK[1] \]

✓ Sympy. Time used: 0.881 (sec). Leaf size: 5

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

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