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

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

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

\frac{d y}{d x} + y \cdot 1 + x^{2} = 0

y = - e^{- x 1 + x^{2} + c_{1}} (x - 1 + x^{2})

Solution steps

\frac{d y}{d x} + y \cdot 1 + x^{2} = 0

Solve separable ODE:

y = - e^{- x 1 + x^{2} + c_{1}} (x - 1 + x^{2})

y = - e^{- x 1 + x^{2} + c_{1}} (x - 1 + x^{2})

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

f (x) = 9 + 5 x^{2} - 2 x^{3}, at x = a

\int \frac{1}{9 - 36 x ^{2}} d x

\frac{d}{d x} (\frac{4 x}{x + 2})

f (x) = 64 - x^{2}

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