80.9.2 problem 2

Internal problem ID [18593]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter VII. Linear equations of order higher than the first. section 63. Problems at page 196
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 12:03:25 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

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

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

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 41

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

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