Internal problem ID [2165]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 26.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+4 y=5 \sin \left (3 x \right ) {\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve(diff(y(x),x$4)+4*y(x)=5*exp(2*x)*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\cos \left (x \right ) c_{3} +c_{4} \sin \left (x \right )\right ) {\mathrm e}^{-x}+\frac {{\mathrm e}^{2 x} \left (24 \cos \left (3 x \right )-23 \sin \left (3 x \right )\right )}{1105}+{\mathrm e}^{x} \left (\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 64
DSolve[y''''[x]+4*y[x]==5*Exp[2*x]*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{2 x} (24 \cos (3 x)-23 \sin (3 x))}{1105}+c_1 e^{-x} \cos (x)+c_4 e^x \cos (x)+c_2 e^{-x} \sin (x)+c_3 e^x \sin (x) \]