75.19.16 problem 633

Internal problem ID [17061]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 633
Date solved : Monday, March 31, 2025 at 03:39:39 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y&=2 \ln \left (x \right )^{2}+12 x \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)+2*y(x) = 2*ln(x)^2+12*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{x^{2}}+2 x +\frac {7}{2}+\frac {c_1}{x}-3 \ln \left (x \right )+\ln \left (x \right )^{2} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 32

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

\[ y(x)\to \frac {c_1}{x^2}+2 x+\log ^2(x)-3 \log (x)+\frac {c_2}{x}+\frac {7}{2} \]

✓ Sympy. Time used: 0.284 (sec). Leaf size: 27

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

\[ y{\left (x \right )} = \frac {C_{1}}{x^{2}} + \frac {C_{2}}{x} + 2 x + \log {\left (x \right )}^{2} - 3 \log {\left (x \right )} + \frac {7}{2} \]