83.49.16 problem Ex 16 page 132

Internal problem ID [19558]
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 16 page 132
Date solved : Monday, March 31, 2025 at 07:33:21 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=8 x^{3} \sin \left (x^{2}\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=x*diff(diff(y(x),x),x)-diff(y(x),x)-4*x^3*y(x) = 8*x^3*sin(x^2); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 29

ode=x*D[y[x],{x,2}]-D[y[x],x]-4*x^3*y[x]==8*x^3*Sin[x^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\sin \left (x^2\right )+c_1 \cosh \left (x^2\right )+i c_2 \sinh \left (x^2\right ) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-4*x**3*y(x) - 8*x**3*sin(x**2) + x*Derivative(y(x), (x, 2)) - Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x*(-4*x**2*y(x) - 8*x**2*sin(x**2) + Derivative(y(x), (x, 2))) + Derivative(y(x), x) cannot be solved by the factorable group method