60.3.416 problem 1433

Internal problem ID [11412]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1433
Date solved : Sunday, March 30, 2025 at 08:21:12 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }&=-\frac {\sin \left (x \right ) y^{\prime }}{\cos \left (x \right )}-\frac {\left (2 x^{2}+x^{2} \sin \left (x \right )^{2}-24 \cos \left (x \right )^{2}\right ) y}{4 x^{2} \cos \left (x \right )^{2}}+\sqrt {\cos \left (x \right )} \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 28

ode:=diff(diff(y(x),x),x) = -sin(x)/cos(x)*diff(y(x),x)-1/4*(2*x^2+x^2*sin(x)^2-24*cos(x)^2)/x^2/cos(x)^2*y(x)+cos(x)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sqrt {\cos \left (x \right )}\, \left (4 c_1 \,x^{5}-x^{4}+4 c_2 \right )}{4 x^{2}} \]

✓ Mathematica. Time used: 0.133 (sec). Leaf size: 35

ode=D[y[x],{x,2}] == Sqrt[Cos[x]] - (Sec[x]^2*(2*x^2 - 24*Cos[x]^2 + x^2*Sin[x]^2)*y[x])/(4*x^2) - Tan[x]*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\left (4 c_2 x^5-5 x^4+20 c_1\right ) \sqrt {\cos (x)}}{20 x^2} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(sin(x)*Derivative(y(x), x)/cos(x) - sqrt(cos(x)) + Derivative(y(x), (x, 2)) + (x**2*sin(x)**2 + 2*x**2 - 24*cos(x)**2)*y(x)/(4*x**2*cos(x)**2),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out