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Solve the differential equation

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Reference no: EM132599869

QUESTION 1  Show that the differential equation (3x2y + ey)dx + (x3 + xey - 2y)dy = 0 is exact and solve it.

QUESTION 2 Solve the differential equation dy/dx + y cot x = cos x, subject to the initial condition y(Π/6) = 9/4.

QUESTION 3 Solve the differential equation x2y - x3 dy/dx = y4 cos x

QUESTION 4 Determine the general solution of the differential equation y′′ - 2y′ - 8y = xe-2x, using the method of undetrmined coefficients.

QUESTION 5 Given the differential equation, y′′ + y = sec x, find its general solution via the method of variation of parameters.

QUESTION 6 Determine the general solution to x2y′′ + 3xy′ + y = 4 ln x , x > 0, using the method of reduction of order given that y1(x) = x-1 is a solution to the homogeneous part.

QUESTION 7 Use Laplace transforms to solve the initial value problem, y′′ = 3y′ + 2y = e3x, y(0) = 1, y′(0) = 0.

Reference no: EM132599869

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