Question

y=C₁eˣ+C₂e⁻²ˣ is a two-parameter family of solutions of the second-order differential equation y′′+y′-2y=0. Find C₁ and C₂ so that the solution satisfies the boundary conditions.

Answer 1

To find the values of C₁ and C₂ that satisfy the boundary conditions for the given differential equation y′′+y′-2y=0, substitute the values of the components into the general solution y=C₁eˣ+C₂e⁻²ˣ and simplify.

Step-by-step explanation:

The given second-order differential equation is y′′+y′-2y=0. The general solution to this equation is y=C₁eˣ+C₂e⁻²ˣ, where C₁ and C₂ are constants. To find the values of C₁ and C₂ that satisfy the boundary conditions, we need to use the given information about the components. By substituting the values of the components into the general solution and simplifying, we can find the values of C₁ and C₂.