Internal problem ID [9874]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1551.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime \prime \prime }-2 \left (\nu ^{2} x^{2}+6\right ) y^{\prime \prime }+\nu ^{2} \left (\nu ^{2} x^{2}+4\right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 62
dsolve(x^2*diff(y(x),x$4)-2*(nu^2*x^2+6)*diff(y(x),x$2)+nu^2*(nu^2*x^2+4)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (c_{4} \nu ^{2} x^{3}+6 c_{4} \nu \,x^{2}+15 c_{4} x +c_{2} \right ) {\mathrm e}^{-x \nu }+{\mathrm e}^{x \nu } \left (c_{3} \nu ^{2} x^{3}-6 c_{3} \nu \,x^{2}+15 c_{3} x +c_{1} \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.197 (sec). Leaf size: 84
DSolve[x^2*y''''[x]-2*(nu^2*x^2+6)*y''[x]+nu^2*(nu^2*x^2+4)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-\nu x} \left (c_3 \left (-\nu ^2 x^3+\nu ^2-6 \nu x^2+6 \nu -15 x+15\right )+e^{2 \nu x} \left (c_4 \left (-\nu ^2 x^3+\nu ^2+6 \nu x^2-6 \nu -15 x+15\right )+c_2\right )+c_1\right )}{x} \]