Internal problem ID [11827]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 53.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y=\cos \left (x \right )^{2}-\cosh \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 56
dsolve(diff(y(x),x$4)+3*diff(y(x),x$2)-4*y(x)=cos(x)^2-cosh(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{8}+\frac {\left (10 x +200 c_{3} +9\right ) {\mathrm e}^{-x}}{200}+\frac {\left (200 c_{2} -9\right ) \cos \left (2 x \right )}{200}+\frac {\left (-x +40 c_{4} \right ) \sin \left (2 x \right )}{40}+\frac {\left (-10 x +200 c_{1} +9\right ) {\mathrm e}^{x}}{200} \]
✓ Solution by Mathematica
Time used: 0.21 (sec). Leaf size: 75
DSolve[y''''[x]+3*y''[x]-4*y[x]==Cos[x]^2-Cosh[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{400} e^{-x} \left ((-13+400 c_1) e^x \cos (2 x)+2 \left (10 x-25 e^x+e^{2 x} (-10 x+9+200 c_4)-5 e^x (x-40 c_2) \sin (2 x)+9+200 c_3\right )\right ) \]