MATH 3350 Midterm: Math 3350 TTU Exam Past Exam1Solutions
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31 Jan 2019
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In each part, nd the general solution of the given di erential equation. A. dy dx x2 + 2y2 xy u = y/x. We can rewrite the equation as dy dx x y. Let u = y/x (where y is a solution of our equation), then y = xu, so y = u + xu . We substitute this expression for the left-hand side of the equation, and rewrite the equation as u + x du dx. Subtracting u from both sides of the equation, we get x du dx. Putting the right-hand side over a common denominator gives x du dx u2 + 1 u. Separating the variables in this equation, we get u. 1 + u2 du = z dx x. The integral on the left can be done by the simple substitution v = 1 + u2. 2 ln|1 + u2| = ln|x| + c.
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