60.3.161 problem 1175

Internal problem ID [11157]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1175
Date solved : Sunday, March 30, 2025 at 07:44:25 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y-x \sin \left (x \right )-\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right )&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 29

ode:=x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)-4*y(x)-x*sin(x)-(a*x^2+12*a+4)*cos(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-2 a -1\right ) \sin \left (x \right )+c_2 \,x^{5}-a x \cos \left (x \right )+c_1}{x} \]

✓ Mathematica. Time used: 0.377 (sec). Leaf size: 92

ode=(-4 - 12*a - a*x^2)*Cos[x] - x*Sin[x] - 4*y[x] - 2*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^5 \int _1^x\frac {\cos (K[2]) \left (a \left (K[2]^2+12\right )+4\right )+K[2] \sin (K[2])}{5 K[2]^5}dK[2]+\int _1^x\frac {1}{5} \left (-\cos (K[1]) \left (a \left (K[1]^2+12\right )+4\right )-K[1] \sin (K[1])\right )dK[1]+c_2 x^5+c_1}{x} \]

✓ Sympy. Time used: 1.346 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x*sin(x) - 2*x*Derivative(y(x), x) - (a*x**2 + 12*a + 4)*cos(x) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + C_{2} x^{5} - a x \cos {\left (x \right )} - 2 a \sin {\left (x \right )} - \sin {\left (x \right )}}{x} \]