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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

y = x^{- \frac{1}{2}}

\frac{d}{d x} (x^{2} \cdot y^{2})

\int \frac{1}{9 - 16 x ^{2}} d x

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\int 5 csc^{2} (x) d x

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