28.2.53 problem 53

Internal problem ID [4496]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 53
Date solved : Monday, January 27, 2025 at 09:21:41 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=72 \,{\mathrm e}^{3 x}+729 x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 45

dsolve(diff(y(x),x$4)-18*diff(y(x),x$2)+81*y(x)=72*exp(3*x)+729*x^2,y(x), singsol=all)
 

\[ y \left (x \right ) = 4+\frac {\left (1+6 x^{2}+2 \left (-2+3 c_4 \right ) x +6 c_{2} \right ) {\mathrm e}^{3 x}}{6}+\left (x c_3 +c_{1} \right ) {\mathrm e}^{-3 x}+9 x^{2} \]

✓ Solution by Mathematica

Time used: 0.307 (sec). Leaf size: 48

DSolve[D[y[x],{x,4}]-18*D[y[x],{x,2}]+81*y[x]==72*Exp[3*x]+729*x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 9 x^2+e^{3 x} \left (x^2+\left (-\frac {2}{3}+c_4\right ) x+\frac {1}{6}+c_3\right )+e^{-3 x} (c_2 x+c_1)+4 \]