40.8.4 problem 19

Internal problem ID [6704]
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 : 19
Date solved : Monday, January 27, 2025 at 02:24:28 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+12 y^{\prime \prime }-8 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

dsolve(diff(y(x),x$4)-6*diff(y(x),x$3)+12*diff(y(x),x$2)-8*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 43

DSolve[D[y[x],{x,4}]-6*D[y[x],{x,3}]+12*D[y[x],{x,2}]-8*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{2 x} \left (c_3 \left (2 x^2-2 x+1\right )+c_2 (2 x-1)+2 c_1\right )+c_4 \]