Show that the DE (10 + 6y)dx + (6x + 18y)dy = 0 is exact. Explain why the solutions a) following implicit equation satisfy DE 10x + 6xy + 9y? = c. b) Y1 (0) = 1 and y2(2) = 2. Verify that yı and y2 satisfy the same implicit equation in a). Can you Consider y, and y2 two solutions of the DE (10 + 6y)dx + (6x + 18y)dy = 0 such that determine explicitly y, and y2 with their domains?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.