77.49.17 problem Ex 17 page 132

Internal problem ID [20914]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VIII. Linear equations of second order
Problem number : Ex 17 page 132
Date solved : Thursday, October 02, 2025 at 06:48:51 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 \cos \left (x \right )^{3} y&=2 \cos \left (x \right )^{5} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 30

ode:=cos(x)*diff(diff(y(x),x),x)+sin(x)*diff(y(x),x)-2*y(x)*cos(x)^3 = 2*cos(x)^5; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sinh \left (\sin \left (x \right ) \sqrt {2}\right ) c_2 +\cosh \left (\sin \left (x \right ) \sqrt {2}\right ) c_1 +\frac {1}{2}-\frac {\cos \left (2 x \right )}{2} \]

✓ Mathematica. Time used: 10.019 (sec). Leaf size: 167

ode=Cos[x]*D[y[x],{x,2}]+Sin[x]*D[y[x],x]-2*y[x]*Cos[x]^3==2*Cos[x]^5; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \cos \left (\sqrt {-\cos (2 x)-1} \tan (x)\right ) \int _1^x\cos ^2(K[1]) \sqrt {-\cos (2 K[1])-1} \sin \left (\sqrt {-\cos (2 K[1])-1} \tan (K[1])\right )dK[1]+\sin \left (\sqrt {-\cos (2 x)-1} \tan (x)\right ) \int _1^x-\cos ^2(K[2]) \sqrt {-\cos (2 K[2])-1} \cos \left (\sqrt {-\cos (2 K[2])-1} \tan (K[2])\right )dK[2]+c_1 \cos \left (\sqrt {-\cos (2 x)-1} \tan (x)\right )+c_2 \sin \left (\sqrt {-\cos (2 x)-1} \tan (x)\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x)*cos(x)**3 + sin(x)*Derivative(y(x), x) - 2*cos(x)**5 + cos(x)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(2*y(x)*cos(x)**2 + 2*cos(x)**4 - Derivative(y(x), (x, 2)))/tan(x) + Derivative(y(x), x) cannot be solved by the factorable group method