Internal problem ID [2114]
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: 42.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$5)+3*diff(y(x),x$4)-15*diff(y(x),x$3)-19*diff(y(x),x$2)+30*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{8 x}+c_{5} {\mathrm e}^{6 x}+c_{1} {\mathrm e}^{5 x}+c_{4} {\mathrm e}^{3 x}+c_{3} \right ) {\mathrm e}^{-5 x} \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 47
DSolve[y'''''[x]+3*y''''[x]-15*y'''[x]-19*y''[x]+30*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{5} c_1 e^{-5 x}-\frac {1}{2} c_2 e^{-2 x}+c_3 e^x+\frac {1}{3} c_4 e^{3 x}+c_5 \]