Internal problem ID [2248]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 24, page 109
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y={\mathrm e}^{2 x} \cos \left (x \right ) x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)-4*y(x)=x*exp(2*x)*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\left (-17 x +76\right ) \cos \left (x \right )+\left (68 x +2\right ) \sin \left (x \right )+289 c_{2} \right ) {\mathrm e}^{2 x}}{289}+{\mathrm e}^{-2 x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 49
DSolve[y''[x]-4*y[x]==x*Exp[2*x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{2 x}+c_2 e^{-2 x}+\frac {1}{289} e^{2 x} (2 (34 x+1) \sin (x)+(76-17 x) \cos (x)) \]