75.19.14 problem 631

Internal problem ID [17059]
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 : 631
Date solved : Monday, March 31, 2025 at 03:39:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y&=x^{2}-2 x +2 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

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

\[ y = x^{\frac {3}{2}+\frac {\sqrt {17}}{2}} c_2 +x^{\frac {3}{2}-\frac {\sqrt {17}}{2}} c_1 -\frac {x^{2}}{4}+\frac {x}{2}-1 \]

✓ Mathematica. Time used: 0.436 (sec). Leaf size: 53

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

\[ y(x)\to c_2 x^{\frac {1}{2} \left (3+\sqrt {17}\right )}+c_1 x^{\frac {3}{2}-\frac {\sqrt {17}}{2}}-\frac {x^2}{4}+\frac {x}{2}-1 \]

✓ Sympy. Time used: 0.507 (sec). Leaf size: 51

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

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x^{- \frac {3}{2} + \frac {\sqrt {17}}{2}} \left (C_{2} x^{\frac {3}{2} + \frac {\sqrt {17}}{2}} - x^{2} + 2 x - 4\right )}{4}}{x^{- \frac {3}{2} + \frac {\sqrt {17}}{2}}} \]