What is the solution for (dy)/(dx)y=7x-5 ?

The solution for (dy)/(dx)y=7x-5 is y=sqrt(7x^2-10x+c_{1)},y=-sqrt(7x^2-10x+c_{1)}

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(dy)/(dx)y=7x-5

\frac{d y}{d x} y = 7 x - 5

y = 7 x^{2} - 10 x + c_{1}, y = - 7 x^{2} - 10 x + c_{1}

Solution steps

\frac{d y}{d x} y = 7 x - 5

Solve separable ODE:

y = 7 x^{2} - 10 x + c_{1}, y = - 7 x^{2} - 10 x + c_{1}

y = 7 x^{2} - 10 x + c_{1}, y = - 7 x^{2} - 10 x + c_{1}

3 x y y^{^{'}} + 4 x - 2 = 0

\frac{d y}{d x} = \frac{( 3 x + x y ^{2} )}{( 2 y - x ^{2} y )}

x (1 + y^{2})^{\frac{1}{2}} d x = y d y

\frac{d y}{d x} = y^{2}, y (0) = 1

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

What is the solution for (dy)/(dx)y=7x-5 ?
The solution for (dy)/(dx)y=7x-5 is y=sqrt(7x^2-10x+c_{1)},y=-sqrt(7x^2-10x+c_{1)}