Let be a twice differentiable function. The integral equation can be rewritten as the following initial value problem:
E) None of the above.

Question

Let  be a twice differentiable function. The integral equation  can be rewritten as the following initial value problem:
E) None of the above.

Quizplus · Accepted Answer

By using integration by parts twice in the given integral equation, we can obtain the equation y'' + 2y' + 2y = 0. Now, by substituting y = e^(rt), we get the characteristic equation r^2 + 2r + 2 = 0. Solving for r, we get r = -1 ± i. Therefore, the general solution of the differential equation is y = e^(-x)(c1*cos(x) + c2*sin(x)). Finally, substituting the given initial conditions, we get the unique solution y = (5/34)*e^(-x)*(4*cos(x) - 3*sin(x)). Thus, the correct answer is A.

Let Be a Twice Differentiable Function