82.30.4 problem Ex. 4

Internal problem ID [18888]
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 77
Problem number : Ex. 4
Date solved : Tuesday, January 28, 2025 at 12:33:30 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y&=\sin \left (3 x \right )-\cos \left (\frac {x}{2}\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.174 (sec). Leaf size: 70

dsolve(diff(y(x),x$3)+y(x)=sin(3*x)-cos(1/2*x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{-x} \left (730 c_{2} {\mathrm e}^{\frac {3 x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right )+730 c_3 \,{\mathrm e}^{\frac {3 x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right )+27 \,{\mathrm e}^{x} \cos \left (3 x \right )+{\mathrm e}^{x} \sin \left (3 x \right )+\left (-\frac {365 \cos \left (x \right )}{2}+\frac {365 \sin \left (x \right )}{2}-365\right ) {\mathrm e}^{x}+730 c_{1} \right )}{730} \]

✓ Solution by Mathematica

Time used: 1.739 (sec). Leaf size: 87

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

\[ y(x)\to \frac {\sin (x)}{4}+\frac {1}{730} \sin (3 x)-\frac {\cos (x)}{4}+\frac {27}{730} \cos (3 x)+c_1 e^{-x}+c_3 e^{x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_2 e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )-\frac {1}{2} \]