75.6.17 problem 150

Internal problem ID [16702]
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 : 150
Date solved : Monday, March 31, 2025 at 03:06:22 PM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.022 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 19

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

\[ y(x)\to \sin (x) \left (\text {Interval}[\{0,\text {Indeterminate}\},\{\text {Indeterminate},0\}]+\frac {1}{x}\right ) \]

✓ Sympy. Time used: 1.237 (sec). Leaf size: 7

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

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