23.3.161 problem 163

Internal problem ID [5875]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 163
Date solved : Friday, October 03, 2025 at 01:44:58 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 3 y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.066 (sec). Leaf size: 25

ode:=3*y(x)+2*tan(x)*diff(y(x),x)+diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-2 c_2 \cos \left (x \right )^{2}-c_2 \right ) \sin \left (x \right )+c_1 \cos \left (x \right )^{3} \]

✓ Mathematica. Time used: 0.096 (sec). Leaf size: 33

ode=3*y[x] + 2*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 \cos ^3(x)-\frac {1}{3} c_2 \sqrt {\sin ^2(x)} (\cos (2 x)+2) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*y(x) + 2*tan(x)*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False