40.8.9 problem 24

Internal problem ID [6709]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 13. Homogeneous Linear equations with constant coefficients. Supplemetary problems. Page 86
Problem number : 24
Date solved : Monday, January 27, 2025 at 02:24:35 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x$4)-6*diff(y(x),x$3)+13*diff(y(x),x$2)-12*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 29

DSolve[D[y[x],{x,4}]-6*D[y[x],{x,3}]+13*D[y[x],{x,2}]-12*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (c_3 e^x+x \left (c_4 e^x+c_2\right )+c_1\right ) \]