Internal problem ID [10312]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 60.
Exact equation. Integrating factor. Page 139
Problem number: Ex 4.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _fully, _exact, _linear]]
Solve \begin {gather*} \boxed {\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 y^{\prime } x +4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 47
dsolve((x^3-x)*diff(y(x),x$3)+(8*x^2-3)*diff(y(x),x$2)+14*x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{3}}{\sqrt {x +1}\, \sqrt {x -1}\, x}+\frac {c_{1}}{x}+\frac {c_{2} \ln \left (x +\sqrt {x^{2}-1}\right )}{x \sqrt {x^{2}-1}} \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 51
DSolve[(x^3-x)*y'''[x]+(8*x^2-3)*y''[x]+14*x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-\frac {c_2}{\sqrt {x^2-1}}+\frac {c_3 \log \left (\sqrt {x^2-1}-x\right )}{\sqrt {x^2-1}}+c_1}{x} \\ \end{align*}