Internal problem ID [2212]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 23, page 106
Problem number: 11.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y=4 \,{\mathrm e}^{x}+3 \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(diff(y(x),x$4)+3*diff(y(x),x$2)-4*y(x)=4*exp(x)+3*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-3+25 c_{2} \right ) \cos \left (2 x \right )}{25}+\frac {\left (-3 x +20 c_{4} \right ) \sin \left (2 x \right )}{20}+c_{3} {\mathrm e}^{-x}+\frac {2 \,{\mathrm e}^{x} \left (x +\frac {5 c_{1}}{2}-\frac {9}{10}\right )}{5} \]
✓ Solution by Mathematica
Time used: 0.17 (sec). Leaf size: 55
DSolve[y''''[x]+3*y''[x]-4*y[x]==4*Exp[x]+3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 e^x x}{5}-\frac {9 e^x}{25}-\frac {\cos (x)}{2}+c_3 e^{-x}+c_4 e^x+c_1 \cos (2 x)+c_2 \sin (2 x) \]