9.2.17 problem problem 29

Internal problem ID [951]
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 29
Date solved : Wednesday, February 05, 2025 at 04:51:17 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+27 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 37

dsolve(diff(y(x),x$3)+27*y(x)=0,y(x), singsol=all)
 

\[ y = \left (c_2 \,{\mathrm e}^{\frac {9 x}{2}} \sin \left (\frac {3 \sqrt {3}\, x}{2}\right )+c_3 \,{\mathrm e}^{\frac {9 x}{2}} \cos \left (\frac {3 \sqrt {3}\, x}{2}\right )+c_1 \right ) {\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 56

DSolve[D[y[x],{x,3}]+27*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (c_3 e^{9 x/2} \cos \left (\frac {3 \sqrt {3} x}{2}\right )+c_2 e^{9 x/2} \sin \left (\frac {3 \sqrt {3} x}{2}\right )+c_1\right ) \]