77.1.113 problem 141 (a) (page 205)

Internal problem ID [17932]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 141 (a) (page 205)
Date solved : Monday, March 31, 2025 at 04:51:48 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 21

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

\[ y = x^{3}+c_1 \,x^{2}+c_2 \cos \left (x \right )+c_3 \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.971 (sec). Leaf size: 46

ode=(x^2+2)*D[y[x],{x,3}]-2*x*D[y[x],{x,2}]+(x^2+2)*D[y[x],x]-2*x*y[x]==x^4+12; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^3+\frac {c_1 x^2}{2}+\frac {1}{2} i c_2 e^{-i x}-\frac {1}{4} c_3 e^{i x} \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4 - 2*x*y(x) - 2*x*Derivative(y(x), (x, 2)) + (x**2 + 2)*Derivative(y(x), x) + (x**2 + 2)*Derivative(y(x), (x, 3)) - 12,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x**4 - x**2*Derivative(y(x), (x, 3)) + 2*x*y(x) + 2*x*Derivative(y(x), (x, 2)) - 2*Derivative(y(x), (x, 3)) + 12)/(x**2 + 2) cannot be solved by the factorable group method