What is the solution for 2x(y+1)+(x^2+6)(dy)/(dx)=0 ?

The solution for 2x(y+1)+(x^2+6)(dy)/(dx)=0 is y=(c_{1})/(x^2+6)-1

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2x(y+1)+(x^2+6)(dy)/(dx)=0

2 x (y + 1) + (x^{2} + 6) \frac{d y}{d x} = 0

y = \frac{c _{1}}{x ^{2} + 6} - 1

Solution steps

2 x (y + 1) + (x^{2} + 6) \frac{d y}{d x} = 0

Solve separable ODE:

y = \frac{c _{1}}{x ^{2} + 6} - 1

y = \frac{c _{1}}{x ^{2} + 6} - 1

y^{^{'}} = - y, y (0) = 5

y^{^{'}} (x) = \frac{y cos ( x )}{1 + 2 y ^{2}}, y (0) = 1

\frac{d t}{d y} = 2 t \cdot y^{2}

7 x y (\frac{d y}{d x}) = 4

\frac{d x}{d t} = \frac{2}{x}, x (0) = 8

What is the solution for 2x(y+1)+(x^2+6)(dy)/(dx)=0 ?
The solution for 2x(y+1)+(x^2+6)(dy)/(dx)=0 is y=(c_{1})/(x^2+6)-1