77.1.111 problem 139 (page 201)

Internal problem ID [17922]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 139 (page 201)
Date solved : Thursday, March 13, 2025 at 11:10:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=2 x^{3} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 14

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

\[ y = x \left (c_{2} x +x^{2}+c_{1} \right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 17

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

\[ y(x)\to x \left (x^2+c_2 x+c_1\right ) \]

✓ Sympy. Time used: 0.307 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = x \left (C_{1} + C_{2} x + x^{2}\right ) \]