54.3.402 problem 1419

Internal problem ID [12697]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1419
Date solved : Wednesday, October 01, 2025 at 02:20:17 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.111 (sec). Leaf size: 12

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

\[ y = x \left (c_1 +c_2 \sin \left (x \right )\right ) \]

✗ Mathematica

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

Not solved

✗ Sympy

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

False