Internal problem ID [295]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with
Constant Coefficients. Page 300
Problem number: problem 20.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 59
dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)+3*diff(y(x),x$2)+2*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+c_{2} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+c_{3} {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) x +c_{4} {\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 52
DSolve[y''''[x]+2*y'''[x]+3*y''[x]+2*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x/2} \left ((c_4 x+c_3) \cos \left (\frac {\sqrt {3} x}{2}\right )+(c_2 x+c_1) \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \\ \end{align*}