Solve the differential equation in Exercises 9–22. dy dy = x²Vy, y> 0 10. dx 9. 2Vxy = 1, x, y > 0 dx dy 11. dx dy 3x e 12. dx dy dy 13. Vycos? Vy dx 14. V2ry dx dy = ev+sin x dx dy 15. Vx dx x > 0 16. (sec x)- dy 2rV1 – y², -1< y < 1 17. dx dy 18. dx e2r-y er+y dy 19. y? Зx2уз —бх? dx dy 20. — ху + 3x — 2у — 6 dx 1 dy х dx dy 22. dx ye + 2Vye 21. et-y + e* + e¯y + 1 %3D

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A: We have to prove the given differential equation to be true.

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A: Given differential equation is,

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Q: Ex.: Solve dx dy 2- dt -x- e' dt dy dt dx +2. +y%3Dt.. dt versity-Civil Enginee & Num. A

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A: We can find the answer as below.

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A: (a)

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Q: Q2: Solve the differential equations: dy y %3D = tan y 1- dx

A: As it is a multiple type question , so I am just solving the first one 1) The differential equation…