Internal problem ID [2112]
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: 40.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 33
dsolve(diff(y(x),x$5)-3*diff(y(x),x$4)-5*diff(y(x),x$3)+15*diff(y(x),x$2)+4*diff(y(x),x)-12*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} {\mathrm e}^{5 x}+c_{2} {\mathrm e}^{4 x}+c_{5} {\mathrm e}^{3 x}+c_{4} {\mathrm e}^{x}+c_{3} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 42
DSolve[y'''''[x]-3*y''''[x]-5*y'''[x]+15*y''[x]+4*y'[x]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (c_2 e^x+e^{3 x} \left (e^x \left (c_5 e^x+c_4\right )+c_3\right )+c_1\right ) \]