82.31.1 problem Ex. 1

Internal problem ID [18889]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. problems at page 79
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:33:30 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 78

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

\[ y \left (x \right ) = \frac {\left (289 c_4 \,{\mathrm e}^{\frac {\sqrt {2}\, x}{2}}+289 c_{2} {\mathrm e}^{-\frac {\sqrt {2}\, x}{2}}\right ) \sin \left (\frac {\sqrt {2}\, x}{2}\right )}{289}+c_3 \,{\mathrm e}^{\frac {\sqrt {2}\, x}{2}} \cos \left (\frac {\sqrt {2}\, x}{2}\right )+c_{1} {\mathrm e}^{-\frac {\sqrt {2}\, x}{2}} \cos \left (\frac {\sqrt {2}\, x}{2}\right )+\frac {{\mathrm e}^{2 x} \left (17 x -32\right )}{289} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 88

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

\[ y(x)\to \frac {1}{289} e^{2 x} (17 x-32)+e^{-\frac {x}{\sqrt {2}}} \left (c_1 e^{\sqrt {2} x}+c_2\right ) \cos \left (\frac {x}{\sqrt {2}}\right )+e^{-\frac {x}{\sqrt {2}}} \left (c_4 e^{\sqrt {2} x}+c_3\right ) \sin \left (\frac {x}{\sqrt {2}}\right ) \]