Internal problem ID [2097]
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: 25.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {2 y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(2*diff(y(x),x$3)-diff(y(x),x$2)-2*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{3} {\mathrm e}^{2 x}+c_{1} {\mathrm e}^{\frac {3 x}{2}}+c_{2} \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 30
DSolve[2*y'''[x]-y''[x]-2*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{x/2}+c_2 e^{-x}+c_3 e^x \]