Internal problem ID [2162]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+5 y=2 x -{\mathrm e}^{-4 x}+\sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=2*x-exp(-4*x)+sin(2*x),y(x), singsol=all)
\[ y = {\mathrm e}^{-2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-2 x} \cos \left (x \right ) c_{1} +\frac {\sin \left (2 x \right )}{65}+\frac {2 x}{5}-\frac {8}{25}-\frac {8 \cos \left (2 x \right )}{65}-\frac {{\mathrm e}^{-4 x}}{5} \]
✓ Solution by Mathematica
Time used: 0.784 (sec). Leaf size: 59
DSolve[y''[x]+4*y'[x]+5*y[x]==2*x-Exp[-4*x]+Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 x}{5}-\frac {e^{-4 x}}{5}+\frac {1}{65} \sin (2 x)-\frac {8}{65} \cos (2 x)+c_2 e^{-2 x} \cos (x)+c_1 e^{-2 x} \sin (x)-\frac {8}{25} \]