Internal problem ID [2137]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 18, page 82
Problem number: 21.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-12 y^{\prime }+16 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 41
dsolve(diff(y(x),x$4)-3*diff(y(x),x$3)+4*diff(y(x),x$2)-12*diff(y(x),x)+16*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{4} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {15}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {15}\, x}{2}\right )+{\mathrm e}^{2 x} \left (c_{2} x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 57
DSolve[y''''[x]-3*y'''[x]+4*y''[x]-12*y'[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x/2} \left (e^{5 x/2} (c_4 x+c_3)+c_2 \cos \left (\frac {\sqrt {15} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {15} x}{2}\right )\right ) \]