Internal problem ID [5395]
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.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-y=\sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
dsolve(diff(y(x),x$4)-y(x)=sin(2*x),y(x), singsol=all)
\[ y = \frac {\sin \left (2 x \right )}{15}+\cos \left (x \right ) c_{1} +c_{2} {\mathrm e}^{x}+c_{3} \sin \left (x \right )+c_{4} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 37
DSolve[y''''[x]-y[x]==Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^x+c_3 e^{-x}+c_4 \sin (x)+\cos (x) \left (\frac {2 \sin (x)}{15}+c_2\right ) \]