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Academic year: 2021

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Name: Perm number:

Midterm – in-class part

Time: 75 minutes 1. (25 points) Find all solutions to the equation

dy

dx = 2xy2− x2dy dx.

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2. (25 points) Find all solutions to the equation

xdy

dx − y = 2x3.

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3. (25 points) Find all solutions to the equation

4x3+ 6xy3+ (9x2y2+ 3)dy dx = 0.

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4. (25 points) The function

y(x) = 12x + 7 144 is one of the solutions to the equation

y00− 7y0+ 12y = x.

Find a solution that satisfies y(0) = 31447 and y0(0) = 1114412.

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5. (bonus 25 points) Find all solutions to the equation

(1 − x2y) + x2(y − x)dy dx = 0.

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