56.3.18 problem 18
Internal
problem
ID
[8876]
Book
:
Own
collection
of
miscellaneous
problems
Section
:
section
3.0
Problem
number
:
18
Date
solved
:
Monday, January 27, 2025 at 05:11:32 PM
CAS
classification
:
[[_3rd_order, _with_linear_symmetries]]
\begin{align*} x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=0 \end{align*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 184
dsolve(x^4*diff(y(x),x$3)+x^3*diff(y(x),x$2)+x^2*diff(y(x),x)+x*y(x)= 0,y(x), singsol=all)
\[
y = c_{1} x^{-\frac {\left (188+12 \sqrt {249}\right )^{{2}/{3}}-4 \left (188+12 \sqrt {249}\right )^{{1}/{3}}-8}{6 \left (188+12 \sqrt {249}\right )^{{1}/{3}}}}+c_{2} x^{\frac {-8+\left (188+12 \sqrt {249}\right )^{{2}/{3}}+8 \left (188+12 \sqrt {249}\right )^{{1}/{3}}}{12 \left (188+12 \sqrt {249}\right )^{{1}/{3}}}} \sin \left (\frac {\sqrt {3}\, \left (\left (188+12 \sqrt {3}\, \sqrt {83}\right )^{{2}/{3}}+8\right ) \ln \left (x \right )}{12 \left (188+12 \sqrt {3}\, \sqrt {83}\right )^{{1}/{3}}}\right )+c_3 \,x^{\frac {-8+\left (188+12 \sqrt {249}\right )^{{2}/{3}}+8 \left (188+12 \sqrt {249}\right )^{{1}/{3}}}{12 \left (188+12 \sqrt {249}\right )^{{1}/{3}}}} \cos \left (\frac {\sqrt {3}\, \left (\left (188+12 \sqrt {3}\, \sqrt {83}\right )^{{2}/{3}}+8\right ) \ln \left (x \right )}{12 \left (188+12 \sqrt {3}\, \sqrt {83}\right )^{{1}/{3}}}\right )
\]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 81
DSolve[x^4*D[y[x],{x,3}]+x^3*D[y[x],{x,2}]+x^2*D[y[x],x]+x*y[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\[
y(x)\to c_1 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}+1\&,1\right ]}+c_3 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}+1\&,3\right ]}+c_2 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+2 \text {$\#$1}+1\&,2\right ]}
\]