Internal problem ID [2109]
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: 37.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime \prime }+2 y^{\prime \prime }-4 y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(4*diff(y(x),x$3)+2*diff(y(x),x$2)-4*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{\frac {x}{2}}+c_{2} {\mathrm e}^{\frac {\left (\sqrt {3}-1\right ) x}{2}}+c_{3} {\mathrm e}^{-\frac {\left (1+\sqrt {3}\right ) x}{2}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 50
DSolve[4*y'''[x]+2*y''[x]-4*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-\frac {1}{2} \left (1+\sqrt {3}\right ) x}+c_2 e^{\frac {1}{2} \left (\sqrt {3}-1\right ) x}+c_3 e^{x/2} \]