54.3.172 problem 1186

Internal problem ID [12467]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1186
Date solved : Wednesday, October 01, 2025 at 01:45:26 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y-\sin \left (x \right ) x^{3}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 32

ode:=x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+8*y(x)-sin(x)*x^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 51

ode=-(x^3*Sin[x]) + 8*y[x] - 5*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.904 (sec). Leaf size: 42

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3*sin(x) + x**2*Derivative(y(x), (x, 2)) - 5*x*Derivative(y(x), x) + 8*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} \left (C_{1} + C_{2} x^{2} - \frac {x \left (x \left (2 \log {\left (x \right )} - \log {\left (x^{2} \right )} - 2 \operatorname {Ci}{\left (x \right )}\right ) + 2 \sin {\left (x \right )}\right )}{4} + \frac {\cos {\left (x \right )}}{2}\right ) \]