84.18.4 problem 10.12

Internal problem ID [22201]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 10. Linear differential equations. General remarks. Supplementary problems
Problem number : 10.12
Date solved : Thursday, October 02, 2025 at 08:34:03 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }+2 y&=x^{2}+x +1 \end{align*}

✗ Maple

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+x^2*diff(diff(diff(y(x),x),x),x)+x*diff(diff(y(x),x),x)-exp(x)*diff(y(x),x)+2*y(x) = x^2+x+1; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,4}]+x^2*D[y[x],{x,3}]+x*D[y[x],{x,2}]-Exp[x]*D[y[x],{x,1}]+2*y[x]==x^2+x+1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 3)) - x**2 + x*Derivative(y(x), (x, 2)) - x + 2*y(x) - exp(x)*Derivative(y(x), x) + Derivative(y(x), (x, 4)) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -(x**2*Derivative(y(x), (x, 3)) - x**2 + x*Derivative(y(x), (x, 2)) - x + 2*y(x) + Derivative(y(x), (x, 4)) - 1)*exp(-x) + Derivative(y(x), x) cannot be solved by the factorable group method