Internal problem ID [2138]
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: 22.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime \prime }+12 y^{\prime \prime }-3 y^{\prime }+14 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(4*diff(y(x),x$3)+12*diff(y(x),x$2)-3*diff(y(x),x)+14*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{\frac {15 x}{4}} \sin \left (\frac {\sqrt {15}\, x}{4}\right )+c_{3} {\mathrm e}^{\frac {15 x}{4}} \cos \left (\frac {\sqrt {15}\, x}{4}\right )+c_{1} \right ) {\mathrm e}^{-\frac {7 x}{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 58
DSolve[4*y'''[x]+12*y''[x]-3*y'[x]+14*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 e^{-7 x/2}+c_2 e^{x/4} \cos \left (\frac {\sqrt {15} x}{4}\right )+c_1 e^{x/4} \sin \left (\frac {\sqrt {15} x}{4}\right ) \]