In Problem 1 we saw that cos x and e_x were solutions of the nonlinear equation (y'')² - y² = 0. Verify that sin x and e^-x are also solutions. Without attempting to solve the differential equation, discuss how these explicit solutions can be found by using knowledge about linear equations. Without attempting to verify, discuss why the linear combinations y = c₁e^x + c₂e^-x + c₃ cos x + c₄ sin x and y = c₂e^-x + c₄ sin x are not, in general, solutions, but the two special linear combinations y = c₁e^x + c₂e^-x and y = c₃ cos x + c₄ sin x must satisfy the differential equation.