Differential Equations Final Exam - Math 385 Spring 2007

1.	Solve the initial value problem y ’ - xy^2 = 2 x y , y(1) = 1 Hint: Separate Variables Answer: y(x) = 2 / (3 ^1-x*x - 1)
2.	Find the general solution to the equation x(x – 1)y’ + y^3 = xy Hint: Bernoulli eq Answer: y^2(x) = (x – 1^)2 / ( 2x - 2 ln |x| + C )
3.	Find the general solution to the equation 3x^2(1 + lny)dx + (x^3/y – 2y) dy = 0 Hint: exact Answer: x^3 (1 + ln y) – y^2 = C
4.	Solve the initial value problem d^3y/dx^3 - 9 dy/dx = 0 y(0) = -1, dy(0)/dx = -1, d^2y(0)/dx^2 = 1 Answer: y(x) = - 10/9 - e^3x / 9 + 2 e^-3x / 9
5.	Find the general solution to the equation d^2y/dx^2 - 3 dy/dx + 2 y = x e^x Answer: y(x) = C1e^x + C2e^2x - ( x^2/2 + x ) e^x Click here to continue with this exam.

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