Differential Equations Final Exam - Math 385 Spring 2007

1.	Solve the initial value problem y ’ + 16y^2 = x y^2 , y(1) = 1 Hint: Separate Variables Answer: y = -1 / [ x^2/2 - 16x + 29/2]
2.	Find the general solution to the equation y ’ + y = xy^5 Hint: Bernoullie D.E. Answer: 1/y^4 = x + ¼ + Ce^4x
3.	Find the general solution to the equation x/[√(1 + x^2)]dx = (xdy + ydx) Hint: xdy + ydx = d(xy) Answer: √(1 + x^2) = xy + C
4.	Solve the initial value problem d^3y/dx^3 + 4 dy/dx = 0 y(0) = 1, dy(0)/dx = -1, d^2y(0)/dx^2 = 3 Answer: y(x) = 7/4 - (3/4) cos(2x) - (1/2) sin(2x)
5.	Find the general solution to the equation d^2y/dx^2 - 16 y = e^4x + sin 2x Hint: Roots of characteristic equation are r = ± 4 Answer: y(x) = C1e^4x + C2e^-4x + (1/8)xe^4x - (1/20)sin(2x) Click here to continue with this exam.

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