82.33.16 problem Ex. 16

Internal problem ID [18909]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 16
Date solved : Tuesday, January 28, 2025 at 12:34:14 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

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

\[ y \left (x \right ) = \left (c_{1} x -2 c_{1} +c_{2} \right ) {\mathrm e}^{x}+\frac {x^{3}}{6}+x^{2}+c_3 x +c_4 \]

✓ Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 37

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

\[ y(x)\to \frac {x^3}{6}+x^2+c_4 x+c_1 e^x+c_2 e^x (x-2)+c_3 \]