82.29.2 problem Ex. 3

Internal problem ID [18884]
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 76
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:33:23 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+8 y&=x^{4}+2 x +1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 53

dsolve(diff(y(x),x$3)+8*y(x)=x^4+2*x+1,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (8 c_{2} {\mathrm e}^{3 x} \cos \left (\sqrt {3}\, x \right )+8 c_3 \,{\mathrm e}^{3 x} \sin \left (\sqrt {3}\, x \right )+\left (x^{4}-x +1\right ) {\mathrm e}^{2 x}+8 c_{1} \right ) {\mathrm e}^{-2 x}}{8} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 54

DSolve[D[y[x],{x,3}]+8*y[x]==x^4+2*x+1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} \left (x^4-x+1\right )+c_1 e^{-2 x}+c_3 e^x \cos \left (\sqrt {3} x\right )+c_2 e^x \sin \left (\sqrt {3} x\right ) \]