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Solve the following D.E's (dy)/(dx) = ...

Solve the following D.E's
`(dy)/(dx) = (2x+y+3)/(2y+x+1)`

Text Solution

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The correct Answer is:
`(x+y+(4)/(3))(x-y+2)^(3) = c`
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Find the general solution of the following D.E's (i) (dy)/(dx) = (x-y+3)/(2x-2y+5) (ii) (x-y)dy = (x+y+1) dx

Find the order and degree of the following D.E's (i) (d^(2)y)/(dx^(2)) + 2((dy)/(dx))^(2) + 5y = 0 (ii) 2(d^(2)y)/(dx^(2)) = (5+(dy)/(dx))^((5)/(3)) (iii) 1+((d^(2)y)/(dx^(2)))^(2) = [2+((dy)/(dx))^(2)]^((3//2)) (iv) [(d^(2)y)/(dx^(2))+((dy)/(dx))^(3)]^((6/(5)) = 6y (v) [((dy)/(dx))^(2) + (d^(2)y)/(dx^(2))]^((7)/(3)) = (d^(3y))/(dx^(3)) (vi) [((dy)/(dx))^((1)/(2)) + ((d^(2)y)/(dx^(2)))^((1)/(2))]^((1)/(4)) = 0 (vii) (d^(2)y)/(dx^(2)) + p^(2)y = 0 (viii) ((d^(3)y)/(dx^(3)))^(2) -3((dy)/(dx))^(2) - e^(x) = 4

Solve (dy)/(dx)=(y^(2)+2y)/(x-1)