77.1.119 problem 146 (page 213)

Internal problem ID [17930]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 146 (page 213)
Date solved : Thursday, March 13, 2025 at 11:10:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=diff(diff(y(x),x),x)*sin(x)^2+sin(x)*cos(x)*diff(y(x),x) = y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \csc \left (x \right ) \left (c_{1} +c_{2} +\left (c_{1} -c_{2} \right ) \cos \left (x \right )\right ) \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 25

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

\[ y(x)\to \frac {c_1-i c_2 \cos (x)}{\sqrt {\sin ^2(x)}} \]

✗ Sympy

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

NotImplementedError : The given ODE -(y(x) - sin(x)**2*Derivative(y(x), (x, 2)))/(sin(x)*cos(x)) + Derivative(y(x), x) cannot be solved by the factorable group method