Internal problem ID [2192]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 19.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y=\sin \left (2 x \right ) {\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)-2*y(x)=exp(-x)*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\sqrt {2}\, x} c_{1} +c_{2} {\mathrm e}^{\sqrt {2}\, x}+\frac {4 \,{\mathrm e}^{-x} \left (\cos \left (2 x \right )-\frac {5 \sin \left (2 x \right )}{4}\right )}{41} \]
✓ Solution by Mathematica
Time used: 0.235 (sec). Leaf size: 57
DSolve[y''[x]-2*y[x]==Exp[-x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {5}{41} e^{-x} \sin (2 x)+\frac {4}{41} e^{-x} \cos (2 x)+c_1 e^{\sqrt {2} x}+c_2 e^{-\sqrt {2} x} \]