Internal problem ID [9092]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1513.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime } x^{3}-4 x^{2} y^{\prime \prime }+\left (x^{2}+8\right ) x y^{\prime }-2 \left (x^{2}+4\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 20
dsolve(x^3*diff(diff(diff(y(x),x),x),x)-4*x^2*diff(diff(y(x),x),x)+(x^2+8)*x*diff(y(x),x)-2*(x^2+4)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x^{2}+x \sin \relax (x ) c_{2}+c_{3} \cos \relax (x ) x \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 23
DSolve[-2*(4 + x^2)*y[x] + x*(8 + x^2)*y'[x] - 4*x^2*y''[x] + x^3*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (c_1 x+c_3 \cos (x)-c_2 \sin (x)) \\ \end{align*}