Internal problem ID [2106]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 17, page 78
Problem number: 34.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(2*diff(y(x),x$4)-3*diff(y(x),x$3)-20*diff(y(x),x$2)+27*diff(y(x),x)+18*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-\frac {x}{2}}+c_{3} {\mathrm e}^{2 x}+c_{4} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 40
DSolve[2*y''''[x]-3*y'''[x]-20*y''[x]+27*y'[x]+18*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (c_1 e^{5 x/2}+c_3 e^{5 x}+c_4 e^{6 x}+c_2\right ) \]