Internal problem ID [6456]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 19.
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-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 220
dsolve(x^4*diff(y(x),x$3)+x^3*diff(y(x),x$2)+x^2*diff(y(x),x)+x*y(x)= x,y(x), singsol=all)
\[ y \relax (x ) = 1+c_{1} x^{\frac {\left (188+12 \sqrt {249}\right )^{\frac {2}{3}} \sqrt {249}}{32}-\frac {47 \left (188+12 \sqrt {249}\right )^{\frac {2}{3}}}{96}-\frac {\left (188+12 \sqrt {249}\right )^{\frac {1}{3}}}{6}+\frac {2}{3}}+c_{2} x^{-\frac {\left (188+12 \sqrt {249}\right )^{\frac {2}{3}} \sqrt {249}}{64}+\frac {47 \left (188+12 \sqrt {249}\right )^{\frac {2}{3}}}{192}+\frac {\left (188+12 \sqrt {249}\right )^{\frac {1}{3}}}{12}+\frac {2}{3}} \cos \left (\frac {\left (188+12 \sqrt {249}\right )^{\frac {1}{3}} \sqrt {3}\, \left (3 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}} \sqrt {249}-47 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}}+16\right ) \ln \relax (x )}{192}\right )+c_{3} x^{-\frac {\left (188+12 \sqrt {249}\right )^{\frac {2}{3}} \sqrt {249}}{64}+\frac {47 \left (188+12 \sqrt {249}\right )^{\frac {2}{3}}}{192}+\frac {\left (188+12 \sqrt {249}\right )^{\frac {1}{3}}}{12}+\frac {2}{3}} \sin \left (\frac {\left (188+12 \sqrt {249}\right )^{\frac {1}{3}} \sqrt {3}\, \left (3 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}} \sqrt {249}-47 \left (188+12 \sqrt {249}\right )^{\frac {1}{3}}+16\right ) \ln \relax (x )}{192}\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 82
DSolve[x^4*y'''[x]+x^3*y''[x]+x^2*y'[x]+x*y[x]== x,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 ]}+1 \\ \end{align*}