Internal problem ID [2134]
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: 18.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }-4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x$4)+diff(y(x),x$3)-3*diff(y(x),x$2)-4*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{-2 x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{4} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 64
DSolve[y''''[x]+y'''[x]-3*y''[x]-4*y'[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (c_4 e^{4 x}+c_2 e^{3 x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{3 x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+c_3\right ) \]