Internal problem ID [823]
Book: Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima,
Meade
Section: Chapter 4.2, Higher order linear differential equations. Constant coefficients. page
180
Problem number: 9.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 61
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+3*diff(y(x),x)+y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\left (-2^{\frac {1}{3}}+1\right ) x}+c_{2} {\mathrm e}^{\left (\frac {2^{\frac {1}{3}}}{2}+1\right ) x} \sin \left (\frac {\sqrt {3}\, 2^{\frac {1}{3}} x}{2}\right )+c_{3} {\mathrm e}^{\left (\frac {2^{\frac {1}{3}}}{2}+1\right ) x} \cos \left (\frac {\sqrt {3}\, 2^{\frac {1}{3}} x}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 54
DSolve[y'''[x]-3*y''[x]+3*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \exp \left (x \left (1+\text {Root}\left [\text {$\#$1}^3+2\&,2\right ]\right )\right )+c_1 e^{x-\sqrt [3]{2} x}+c_3 e^{\left (1+\sqrt [3]{-2}\right ) x} \\ \end{align*}