Internal problem ID [9091]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1512.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime } x^{3}+3 x^{2} y^{\prime \prime }+\left (-a^{2}+1\right ) x y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 18
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)+(-a^2+1)*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1}+c_{2} x^{-a}+c_{3} x^{a} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 29
DSolve[(1 - a^2)*x*y'[x] + 3*x^2*y''[x] + x^3*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-c_1 x^{-a}+c_2 x^a+a c_3}{a} \\ \end{align*}