40.11.5 problem 30

Internal problem ID [6739]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary problems. Page 107
Problem number : 30
Date solved : Monday, January 27, 2025 at 02:26:54 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y&=\cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.051 (sec). Leaf size: 48

dsolve(diff(y(x),x$3)+y(x)=cos(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} \left (c_2 \cos \left (\frac {\sqrt {3}\, x}{2}\right ) {\mathrm e}^{\frac {3 x}{2}}+c_3 \sin \left (\frac {\sqrt {3}\, x}{2}\right ) {\mathrm e}^{\frac {3 x}{2}}+\frac {\left (-\sin \left (x \right )+\cos \left (x \right )\right ) {\mathrm e}^{x}}{2}+c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.443 (sec). Leaf size: 68

DSolve[D[y[x],{x,3}]+y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

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