What is the solution for (dy)/(dx)=y^2-y+2 ?

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

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(dy)/(dx)=y^2-y+2

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

y = \frac{tan ( \frac{7 ( x + c _{1} )}{2} ) 7}{2} + \frac{1}{2}

Solution steps

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

Solve separable ODE:

y = \frac{tan ( \frac{7 ( x + c _{1} )}{2} ) 7}{2} + \frac{1}{2}

y = \frac{tan ( \frac{7 ( x + c _{1} )}{2} ) 7}{2} + \frac{1}{2}

y^{^{'}} y^{2} = (t - 2)^{2}

y^{^{'}} - \frac{1}{3} a^{2} y = 0

\frac{d y}{d x} = 10 y - x y + 3 y (x^{2} + 49)

(2 x y^{2} + y^{2} + 3 + 6 x) - (4 x^{2} y + 4 x y) y^{^{'}} = 0

\frac{d y}{d x} = 7 e^{y}

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