9.2.19 problem problem 31

Internal problem ID [953]
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 31
Date solved : Wednesday, February 05, 2025 at 04:51:18 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)+4*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 34

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]+4*D[y[x],x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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