Internal problem ID [2136]
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: 20.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {2 y^{\prime \prime \prime }-3 y^{\prime \prime }+11 y^{\prime }-40 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(2*diff(y(x),x$3)-3*diff(y(x),x$2)+11*diff(y(x),x)-40*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {5 x}{2}}+c_{2} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {31}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {31}\, x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 50
DSolve[2*y'''[x]-3*y''[x]+11*y'[x]-40*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x/2} \left (c_3 e^{3 x}+c_2 \cos \left (\frac {\sqrt {31} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {31} x}{2}\right )\right ) \]