Internal problem ID [9116]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 4, linear fourth order
Problem number: 1537.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-12 y^{\prime \prime }+12 y-16 x^{4} {\mathrm e}^{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 67
dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-12*diff(diff(y(x),x),x)+12*y(x)-16*x^4*exp(x^2)=0,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x^{2}}+c_{1} {\mathrm e}^{\sqrt {6-2 \sqrt {6}}\, x}+c_{2} {\mathrm e}^{\sqrt {6+2 \sqrt {6}}\, x}+c_{3} {\mathrm e}^{-\sqrt {6-2 \sqrt {6}}\, x}+c_{4} {\mathrm e}^{-\sqrt {6+2 \sqrt {6}}\, x} \]
✓ Solution by Mathematica
Time used: 0.794 (sec). Leaf size: 93
DSolve[-16*E^x^2*x^4 + 12*y[x] - 12*y''[x] + Derivative[4][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x^2}+c_1 e^{\sqrt {6-2 \sqrt {6}} x}+c_2 e^{-\sqrt {6-2 \sqrt {6}} x}+c_3 e^{\sqrt {2 \left (3+\sqrt {6}\right )} x}+c_4 e^{-\sqrt {2 \left (3+\sqrt {6}\right )} x} \\ \end{align*}