60.3.62 problem 1067

Internal problem ID [11058]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1067
Date solved : Sunday, March 30, 2025 at 07:41:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime } \tan \left (x \right )-y \cos \left (x \right )^{2}&=0 \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+diff(y(x),x)*tan(x)-y(x)*cos(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{\sin \left (x \right )}+c_2 \,{\mathrm e}^{-\sin \left (x \right )} \]

✓ Mathematica. Time used: 2.778 (sec). Leaf size: 34

ode=-(Cos[x]^2*y[x]) + Tan[x]*D[y[x],x] + D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✗ Sympy

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

False