Internal problem ID [2124]
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: 8.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {4 y^{\left (5\right )}-3 y^{\prime \prime \prime }-y^{\prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(4*diff(y(x),x$5)-3*diff(y(x),x$3)-diff(y(x),x$2)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{5} x +c_{4} \right ) {\mathrm e}^{-\frac {x}{2}}+c_{2} x +c_{3} {\mathrm e}^{x}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.196 (sec). Leaf size: 36
DSolve[4*y'''''[x]-3*y'''[x]-y''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 4 e^{-x/2} (c_2 (x+4)+c_1)+c_3 e^x+c_5 x+c_4 \]