Internal problem ID [14843]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 22.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(9*diff(y(x),x$3)+36*diff(y(x),x$2)+40*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} {\mathrm e}^{-2 x} \sin \left (\frac {2 x}{3}\right )+c_{3} {\mathrm e}^{-2 x} \cos \left (\frac {2 x}{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.242 (sec). Leaf size: 48
DSolve[9*y'''[x]+36*y''[x]+40*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3-\frac {3}{20} e^{-2 x} \left ((c_1+3 c_2) \cos \left (\frac {2 x}{3}\right )+(3 c_1-c_2) \sin \left (\frac {2 x}{3}\right )\right ) \]