54.3.61 problem 1066

Internal problem ID [12356]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1066
Date solved : Wednesday, October 01, 2025 at 01:43:44 AM
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: 0.032 (sec). Leaf size: 15

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);
 

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

✓ Mathematica. Time used: 0.748 (sec). Leaf size: 37

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]
 

\begin{align*} y(x)&\to c_1 \cosh \left (\sqrt {-\sin ^2(x)}\right )+i c_2 \sinh \left (\sqrt {-\sin ^2(x)}\right ) \end{align*}

✗ 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