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

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

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

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

y = e^{\frac{1}{2} a r c t a n (\frac{x}{2}) + c_{1}}

Solution steps

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

Solve separable ODE:

y = e^{\frac{1}{2} a r c t a n (\frac{x}{2}) + c_{1}}

y = e^{\frac{1}{2} a r c t a n (\frac{x}{2}) + c_{1}}

x \to 0 lim (\frac{e ^{x} - 2}{x})

x \to - 8 lim (\frac{8 + x}{8 + x})

\int (x^{4} + x^{3})^{12} (4 x^{3} + 3 x^{2}) d x

cos (2 t)

s^{2} + 4 s + 13 s^{2} + 4 s + 13

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