7.10.10 problem 10

Internal problem ID [280]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.3 (Homogeneous equations with constant coefficients). Problems at page 134
Problem number : 10
Date solved : Monday, January 27, 2025 at 02:43:18 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} 5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 20

dsolve(5*diff(y(x),x$4)+3*diff(y(x),x$3)=0,y(x), singsol=all)
 

\[ y = c_1 +c_2 x +c_3 \,x^{2}+c_4 \,{\mathrm e}^{-\frac {3 x}{5}} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 30

DSolve[5*D[y[x],{x,4}]+3*D[y[x],{x,3}]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {125}{27} c_1 e^{-3 x/5}+x (c_4 x+c_3)+c_2 \]