9.2.5 problem problem 14

Internal problem ID [939]
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 14
Date solved : Wednesday, February 05, 2025 at 04:51:15 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

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

\[ y = {\mathrm e}^{-x} c_1 +c_2 \,{\mathrm e}^{x}+c_3 \sin \left (2 x \right )+c_4 \cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 34

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

\[ y(x)\to c_3 e^{-x}+c_4 e^x+c_1 \cos (2 x)+c_2 \sin (2 x) \]