Internal problem ID [2126]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 18, page 82
Problem number: 10.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(4*diff(y(x),x$3)-8*diff(y(x),x$2)+5*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{\frac {x}{2}}+c_{3} {\mathrm e}^{\frac {x}{2}} x \]
✓ Solution by Mathematica
Time used: 0.002 (sec). Leaf size: 30
DSolve[4*y'''[x]-8*y''[x]+5*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{x/2} \left (c_2 x+c_3 e^{x/2}+c_1\right ) \]