Internal problem ID [2115]
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: 43.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(diff(y(x),x$4)+3*diff(y(x),x$2)-4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} c_{1} +c_{2} {\mathrm e}^{x}+c_{3} \sin \left (2 x \right )+c_{4} \cos \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 34
DSolve[y''''[x]+3*y''[x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 e^{-x}+c_4 e^x+c_1 \cos (2 x)+c_2 \sin (2 x) \]