What is the solution for (dy)/(dx)=(3x-5)/(y-2) ?

The solution for (dy)/(dx)=(3x-5)/(y-2) is y=2+sqrt(3x^2-10x+c_{1)+4},y=2-sqrt(3x^2-10x+c_{1)+4}

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(dy)/(dx)=(3x-5)/(y-2)

\frac{d y}{d x} = \frac{3 x - 5}{y - 2}

y = 2 + 3 x^{2} - 10 x + c_{1} + 4, y = 2 - 3 x^{2} - 10 x + c_{1} + 4

Solution steps

\frac{d y}{d x} = \frac{3 x - 5}{y - 2}

Solve separable ODE:

y = 2 + 3 x^{2} - 10 x + c_{1} + 4, y = 2 - 3 x^{2} - 10 x + c_{1} + 4

y = 2 + 3 x^{2} - 10 x + c_{1} + 4, y = 2 - 3 x^{2} - 10 x + c_{1} + 4

y^{^{'}} = 4 x^{2} y + 5 x y, y (1) = 1

(y) = y^{^{'}}

y^{3} - y^{^{'}} = 0

\frac{d y}{d x} = y \cdot x^{2} - 1.1 \cdot y

(2 x y + 2 x) d x = y d y

What is the solution for (dy)/(dx)=(3x-5)/(y-2) ?
The solution for (dy)/(dx)=(3x-5)/(y-2) is y=2+sqrt(3x^2-10x+c_{1)+4},y=2-sqrt(3x^2-10x+c_{1)+4}