Internal problem ID [2190]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }+2 y=\sin \left ({\mathrm e}^{-x}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=sin(exp(-x)),y(x), singsol=all)
\[ y = \left (c_{1} {\mathrm e}^{x}-{\mathrm e}^{x} \sin \left ({\mathrm e}^{-x}\right )+c_{2} \right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 29
DSolve[y''[x]-3*y'[x]+2*y[x]==Sin[Exp[-x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (-e^x \sin \left (e^{-x}\right )+c_2 e^x+c_1\right ) \]