Consider the following differential equation. (2x - 1) dx + (7y + 5) dy = 0 Let M = 2x 1 and N = 7y + 5. Find the following partial derivatives. My = = 0 Is the given differential equation exact? No Let 0 Yes af = 2x 1. Integrate this partial derivative with respect to x, letting h(y) be an unknown function in y. əx f(x, y) = 2 x - x Find the derivative of h(y). 7y+5 h'(y) = + h(y) Find the general solution of the given differential equation. (If it is not exact, enter NOT.) 7 x²-x + y² + 5y + C x

Consider the following differential equation.
(2x1) dx + (7y + 5) dy = 0
Let M = 2x - 1 and N = 7y + 5. Find the following partial derivatives.
0
My
N₂
=
=
0
Is the given differential equation exact?
Yes
No
Let
af
= 2x - 1. Integrate this partial derivative with respect to x, letting h(y) be an unknown function in y.
əx
2
F(x, y) = x² X
Find the derivative of h(y).
h'(y) = 7y + 5
+ h(y)
Find the general solution of the given differential equation. (If it is not exact, enter NOT.)
x²-x+
71723²
+ 5y + C x

Transcribed Image Text: Consider the following differential equation. (2x1) dx + (7y + 5) dy = 0 Let M = 2x - 1 and N = 7y + 5. Find the following partial derivatives. 0 My N₂ = = 0 Is the given differential equation exact? Yes No Let af = 2x - 1. Integrate this partial derivative with respect to x, letting h(y) be an unknown function in y. əx 2 F(x, y) = x² X Find the derivative of h(y). h'(y) = 7y + 5 + h(y) Find the general solution of the given differential equation. (If it is not exact, enter NOT.) x²-x+ 71723² + 5y + C x

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