Internal problem ID [6455]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 18.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime \prime }+x^{3} y^{\prime \prime }+y^{\prime } x^{2}+x y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 182
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)
\[ y \relax (x ) = c_{1} x^{-\frac {\left (188+12 \sqrt {249}\right )^{\frac {2}{3}}-4 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}}-8}{6 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}}}}+c_{2} x^{\frac {-8+\left (188+12 \sqrt {249}\right )^{\frac {2}{3}}+8 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}}}{12 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}}}} \sin \left (\frac {\left (\left (188+12 \sqrt {249}\right )^{\frac {2}{3}} \sqrt {3}+8 \sqrt {3}\right ) \ln \relax (x )}{12 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}}}\right )+c_{3} x^{\frac {-8+\left (188+12 \sqrt {249}\right )^{\frac {2}{3}}+8 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}}}{12 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}}}} \cos \left (\frac {\left (\left (188+12 \sqrt {249}\right )^{\frac {2}{3}} \sqrt {3}+8 \sqrt {3}\right ) \ln \relax (x )}{12 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}}}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 81
DSolve[x^4*y'''[x]+x^3*y''[x]+x^2*y'[x]+x*y[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 ]} \\ \end{align*}