85.66.4 problem 6 (a)

Internal problem ID [22890]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. C Exercises at page 213
Problem number : 6 (a)
Date solved : Thursday, October 02, 2025 at 09:16:18 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.015 (sec). Leaf size: 15

ode:=sin(x)*diff(diff(y(x),x),x)+(3*sin(x)^2-cos(x))*diff(y(x),x)+2*sin(x)^3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.084 (sec). Leaf size: 20

ode=Sin[x]*D[y[x],{x,2}]+(3*Sin[x]^2-Cos[x])*D[y[x],x]+2*Sin[x]^3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{\cos (x)} \left (c_2 e^{\cos (x)}+c_1\right ) \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE -(2*y(x)*sin(x)**2 + Derivative(y(x), (x, 2)))*sin(x)/(-3*sin(x)