Internal problem ID [10899]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 3(d).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {3 y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(3*diff(y(x),x$4)-2*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{6}\right )+c_{4} {\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.612 (sec). Leaf size: 80
DSolve[3*y''''[x]-2*y''[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 \left (-e^{-x}\right )+\frac {1}{2} e^{x/2} \left (\left (3 c_2-\sqrt {3} c_1\right ) \cos \left (\frac {x}{2 \sqrt {3}}\right )+\left (3 c_1+\sqrt {3} c_2\right ) \sin \left (\frac {x}{2 \sqrt {3}}\right )\right )+c_4 \\ \end{align*}