87.8.17 problem 17
Internal
problem
ID
[23371]
Book
:
Ordinary
differential
equations
with
modern
applications.
Ladas,
G.
E.
and
Finizio,
N.
Wadsworth
Publishing.
California.
1978.
ISBN
0-534-00552-7.
QA372.F56
Section
:
Chapter
2.
Linear
differential
equations.
Exercise
at
page
65
Problem
number
:
17
Date
solved
:
Friday, October 03, 2025 at 08:03:43 AM
CAS
classification
:
[[_3rd_order, _linear, _nonhomogeneous]]
\begin{align*} x y^{\prime \prime \prime }+4 x y^{\prime \prime }-y x&=1 \end{align*}
✓ Maple. Time used: 0.006 (sec). Leaf size: 728
ode:=x*diff(diff(diff(y(x),x),x),x)+4*x*diff(diff(y(x),x),x)-x*y(x) = 1;
dsolve(ode,y(x), singsol=all);
\[
\text {Expression too large to display}
\]
✓ Mathematica. Time used: 0.14 (sec). Leaf size: 470
ode=x*D[y[x],{x,3}]+4*x*D[y[x],{x,2}]-x*y[x]==1;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*} y(x)&\to -\frac {-\text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,3\right ] \exp \left (x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,1\right ]\right ) \operatorname {ExpIntegralEi}\left (\text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,3\right ] x+\text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,2\right ] x+4 x\right )+\text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,2\right ] \exp \left (x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,1\right ]\right ) \operatorname {ExpIntegralEi}\left (\text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,3\right ] x+\text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,2\right ] x+4 x\right )+\text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,3\right ] \exp \left (x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,2\right ]\right ) \operatorname {ExpIntegralEi}\left (-x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,2\right ]\right )-\text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,2\right ] \exp \left (x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,3\right ]\right ) \operatorname {ExpIntegralEi}\left (-x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,3\right ]\right )+\text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,1\right ] \exp \left (x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,3\right ]\right ) \operatorname {ExpIntegralEi}\left (-x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,3\right ]\right )-\text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,1\right ] \exp \left (x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,2\right ]\right ) \operatorname {ExpIntegralEi}\left (-x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,2\right ]\right )}{\sqrt {229}}+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,3\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,2\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3+4 \text {$\#$1}^2-1\&,1\right ]\right ) \end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x*y(x) + 4*x*Derivative(y(x), (x, 2)) + x*Derivative(y(x), (x, 3)) - 1,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
NotImplementedError : solve: Cannot solve -x*y(x) + 4*x*Derivative(y(x), (x, 2)) + x*Derivative(y(x)