Internal problem ID [2111]
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: 39.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)-7*diff(y(x),x$2)-8*diff(y(x),x)+12*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{-3 x}+c_{2} {\mathrm e}^{-2 x}+c_{3} {\mathrm e}^{x}+c_{4} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 35
DSolve[y''''[x]+2*y'''[x]-7*y''[x]-8*y'[x]+12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (c_2 e^x+e^{4 x} \left (c_4 e^x+c_3\right )+c_1\right ) \]