What is the solution for (2x+3)dx+(2y-2)dy=0 ?

The solution for (2x+3)dx+(2y-2)dy=0 is y=1+sqrt(-x^2-3x+c_{1)+1},y=1-sqrt(-x^2-3x+c_{1)+1}

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(2x+3)dx+(2y-2)dy=0

(2 x + 3) d x + (2 y - 2) d y = 0

y = 1 + - x^{2} - 3 x + c_{1} + 1, y = 1 - - x^{2} - 3 x + c_{1} + 1

Solution steps

(2 x + 3) d x + (2 y - 2) d y = 0

Solve separable ODE:

y = 1 + - x^{2} - 3 x + c_{1} + 1, y = 1 - - x^{2} - 3 x + c_{1} + 1

y = 1 + - x^{2} - 3 x + c_{1} + 1, y = 1 - - x^{2} - 3 x + c_{1} + 1

\frac{d}{d x} (e^{- \frac{4}{x}})

y^{^{'}} = \frac{6 x ^{4} + y ^{4}}{x y ^{3}}

\int \frac{7 x ^{2}}{5 - x ^{6}} d x

x = - 3, x = 1, y = e^{x}, y = 1 - e^{x}

x y^{^{'}} + y = e^{x}, y (1) = 3

What is the solution for (2x+3)dx+(2y-2)dy=0 ?
The solution for (2x+3)dx+(2y-2)dy=0 is y=1+sqrt(-x^2-3x+c_{1)+1},y=1-sqrt(-x^2-3x+c_{1)+1}