40.11.4 problem 29

Internal problem ID [6738]
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 : 29
Date solved : Monday, January 27, 2025 at 02:26:53 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 29

dsolve(diff(y(x),x$4)-y(x)=sin(2*x),y(x), singsol=all)
 

\[ y = \frac {\sin \left (2 x \right )}{15}+\cos \left (x \right ) c_1 +{\mathrm e}^{x} c_2 +c_3 \sin \left (x \right )+c_4 \,{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 37

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

\[ y(x)\to c_1 e^x+c_3 e^{-x}+c_4 \sin (x)+\cos (x) \left (\frac {2 \sin (x)}{15}+c_2\right ) \]