60.4.77 problem 1527
Internal
problem
ID
[11528]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
3,
linear
third
order
Problem
number
:
1527
Date
solved
:
Tuesday, January 28, 2025 at 06:06:46 PM
CAS
classification
:
[[_3rd_order, _with_linear_symmetries]]
\begin{align*} \left (x -a \right )^{3} \left (x -b \right )^{3} y^{\prime \prime \prime }-c y&=0 \end{align*}
✓ Solution by Maple
Time used: 0.033 (sec). Leaf size: 437
dsolve((x-a)^3*(x-b)^3*diff(diff(diff(y(x),x),x),x)-c*y(x)=0,y(x), singsol=all)
\[
y = \left (-a +x \right )^{-\frac {2 b}{a -b}} \left (x -b \right )^{\frac {2 a}{a -b}} \left (c_{1} \left (-x +b \right )^{-\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =1\right )}{a -b}} \left (a -x \right )^{\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =1\right )}{a -b}}+c_{2} \left (-x +b \right )^{-\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =2\right )}{a -b}} \left (a -x \right )^{\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =2\right )}{a -b}}+c_3 \left (-x +b \right )^{-\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =3\right )}{a -b}} \left (a -x \right )^{\frac {\operatorname {RootOf}\left (\textit {\_Z}^{3}+\left (-3 a -3 b \right ) \textit {\_Z}^{2}+\left (2 a^{2}+8 a b +2 b^{2}\right ) \textit {\_Z} -4 a^{2} b -4 a \,b^{2}-c , \operatorname {index} =3\right )}{a -b}}\right )
\]
✓ Solution by Mathematica
Time used: 130.117 (sec). Leaf size: 165
DSolve[-(c*y[x]) + (-a + x)^3*(-b + x)^3*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[
y(x)\to c_1 (x-b)^2 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2-2 \text {$\#$1}+\frac {c}{(a-b)^3}\&,1\right ]}+c_2 (x-b)^2 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2-2 \text {$\#$1}+\frac {c}{(a-b)^3}\&,2\right ]}+c_3 (x-b)^2 \left (\frac {x-a}{x-b}\right )^{\text {Root}\left [-\text {$\#$1}^3+3 \text {$\#$1}^2-2 \text {$\#$1}+\frac {c}{(a-b)^3}\&,3\right ]}
\]