64.21.2 problem 1 (b)
Internal
problem
ID
[13663]
Book
:
Differential
Equations
by
Shepley
L.
Ross.
Third
edition.
John
Willey.
New
Delhi.
2004.
Section
:
Chapter
11,
The
nth
order
homogeneous
linear
differential
equation.
Section
11.6,
Exercises
page
567
Problem
number
:
1
(b)
Date
solved
:
Tuesday, January 28, 2025 at 05:54:32 AM
CAS
classification
:
[[_3rd_order, _with_linear_symmetries]]
\begin{align*} t^{3} x^{\prime \prime \prime }-3 t^{2} x^{\prime \prime }+6 t x^{\prime }-6 x&=0 \end{align*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 16
dsolve(t^3*diff(x(t),t$3)-3*t^2*diff(x(t),t$2)+6*t*diff(x(t),t)-6*x(t)=0,x(t), singsol=all)
\[
x \left (t \right ) = t \left (c_{2} t^{2}+c_{1} t +c_{3} \right )
\]
✓ Solution by Mathematica
Time used: 0.030 (sec). Leaf size: 507
DSolve[t^3*D[x[t],{t,3}]-3*t^2*D[x[t],{t,2}]+6*D[x[t],t]-6*x[t]==0,{x[t]},t,IncludeSingularSolutions -> True]
\[
x(t)\to c_3 6^{-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,3\right ]} t^{\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,3\right ]} \, _1F_2\left (-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,3\right ];1+\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,1\right ]-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,3\right ],1+\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,2\right ]-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,3\right ];-\frac {6}{t}\right )+c_2 6^{-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,2\right ]} t^{\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,2\right ]} \, _1F_2\left (-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,2\right ];1+\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,1\right ]-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,2\right ],1-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,2\right ]+\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,3\right ];-\frac {6}{t}\right )+c_1 6^{-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,1\right ]} t^{\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,1\right ]} \, _1F_2\left (-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,1\right ];1-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,1\right ]+\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,2\right ],1-\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,1\right ]+\text {Root}\left [\text {$\#$1}^3-6 \text {$\#$1}^2+5 \text {$\#$1}-6\&,3\right ];-\frac {6}{t}\right )
\]