**MATH - DIFFERENTIAL EQUATION p.2**

Solve the questions below.

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Image transcriptions

Verify that the given differential equation is not exact. (-xy sin(x) + 2y cos(x)) dx + 2x cos(x) dy = 0 If the given DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has N. X Since M and Nx ---Select-- v equal, the equation is not exact. Multiply the given differential equation by the integrating factor #(x, y) = xy and verify that the new equation is exact. If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = N. X = Since M and / ---Select--- v equal, the equation is exact. Solve.

Use a numerical solver and Euler's method to obtain a four-decimal approximation of the indicated value. First use h = 0.1 and then use h = 0.05. y' = (x - y) , y(0) = 0.6; y(0.5) y(0.5) = (h = 0.1) y(0.5) = (h = 0.05) Need Help? Read It

Find the value of k so that the given differential equation is exact. (9xy + cos(y) ) dx + (2kx y - x sin(y) ) dy = 0 K = Need Help? Read It

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