Internal problem ID [2107]
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: 35.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {12 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(12*diff(y(x),x$4)-4*diff(y(x),x$3)-3*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{x}+c_{3} {\mathrm e}^{\frac {5 x}{6}}+c_{1} {\mathrm e}^{\frac {x}{2}}+c_{4} \right ) {\mathrm e}^{-\frac {x}{2}} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 39
DSolve[12*y''''[x]-4*y'''[x]-3*y''[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x/2} \left (3 c_1 e^{5 x/6}+2 c_3 e^x-2 c_2\right )+c_4 \]