82.33.29 problem Ex. 29

Internal problem ID [18922]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 29
Date solved : Tuesday, January 28, 2025 at 12:37:06 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y&={\mathrm e}^{2 x} \sin \left (x \right )+{\mathrm e}^{\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.107 (sec). Leaf size: 68

dsolve(diff(y(x),x$3)+y(x)=exp(2*x)*sin(x)+exp(x/2)*sin(x*sqrt(3)/2),y(x), singsol=all)
 

\[ y \left (x \right ) = -\frac {\left ({\mathrm e}^{\frac {3 x}{2}} \left (x -6 c_3 -2\right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )+{\mathrm e}^{\frac {3 x}{2}} \left (\sqrt {3}\, x -6 c_{2} \right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )+\frac {3 \left (-3 \sin \left (x \right )+11 \cos \left (x \right )\right ) {\mathrm e}^{3 x}}{65}-6 c_{1} \right ) {\mathrm e}^{-x}}{6} \]

✓ Solution by Mathematica

Time used: 0.695 (sec). Leaf size: 136

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

\[ y(x)\to \frac {3}{130} e^{2 x} \sin (x)+\frac {1}{3} e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )-\frac {1}{6} e^{x/2} x \sin \left (\frac {\sqrt {3} x}{2}\right )-\frac {11}{130} e^{2 x} \cos (x)+c_1 e^{-x}-\frac {1}{6} e^{x/2} \left (\sqrt {3} x-6 c_3\right ) \cos \left (\frac {\sqrt {3} x}{2}\right )+c_2 e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right ) \]