32.7.19 problem Exercise 20.20, page 220

Internal problem ID [5934]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 20. Constant coefficients
Problem number : Exercise 20.20, page 220
Date solved : Monday, January 27, 2025 at 01:27:43 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-11 y^{\prime \prime }-12 y^{\prime }+36 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x$4)+2*diff(y(x),x$3)-11*diff(y(x),x$2)-12*diff(y(x),x)+36*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-3 x} \left (\left (c_4 x +c_3 \right ) {\mathrm e}^{5 x}+c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 35

DSolve[D[y[x],{x,4}]+2*D[y[x],{x,3}]-11*D[y[x],{x,2}]-12*D[y[x],x]+36*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (c_3 e^{5 x}+x \left (c_4 e^{5 x}+c_2\right )+c_1\right ) \]