28.2.52 problem 52

Internal problem ID [4495]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 52
Date solved : Monday, January 27, 2025 at 09:21:40 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y&=32 \,{\mathrm e}^{2 x}+16 x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 43

dsolve(diff(y(x),x$4)-8*diff(y(x),x$2)+16*y(x)=32*exp(2*x)+16*x^3,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (3+8 x^{2}+8 \left (c_4 -1\right ) x +8 c_{2} \right ) {\mathrm e}^{2 x}}{8}+\left (x c_3 +c_{1} \right ) {\mathrm e}^{-2 x}+x^{3}+3 x \]

✓ Solution by Mathematica

Time used: 0.315 (sec). Leaf size: 47

DSolve[D[y[x],{x,4}]-8*D[y[x],{x,2}]+16*y[x]==32*Exp[2*x]+16*x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (x^2+3\right )+e^{2 x} \left (x^2+(-1+c_4) x+\frac {3}{8}+c_3\right )+e^{-2 x} (c_2 x+c_1) \]