What is the solution for cot(x)(e-y+1)dx=(1+sin^2(x))dy ?

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

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cot(x)(e-y+1)dx=(1+sin^2(x))dy

cot (x) (e - y + 1) d x = (1 + sin^{2} (x)) d y

y = - \frac{c _{1} sin ^{2} ( x ) + 1}{sin ( x )} + 1 + e

Solution steps

cot (x) (e - y + 1) d x = (1 + sin^{2} (x)) d y

Solve separable ODE:

y = - \frac{c _{1} sin ^{2} ( x ) + 1}{sin ( x )} + 1 + e

y = - \frac{c _{1} sin ^{2} ( x ) + 1}{sin ( x )} + 1 + e

y^{^{'}} arctan (x) - y (1 + x^{2})^{- 1} = 0

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

y^{^{'}} = 14 y + 1

(csc (y)) d x + (cos^{2} (x)) d y = 0

x - 1 \frac{d y}{d x} = \frac{x}{y}, y = 1, x = 2

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