What is the (dy)/(dx)=(ycos(x))/(1+y^2),y(0)=1 ?

The (dy)/(dx)=(ycos(x))/(1+y^2),y(0)=1 is (cos(x))/2

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

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

\frac{cos ( x )}{2}

Solution steps

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

Constant function results in a constant

y (0) = 1

= \frac{1 \cdot cos ( x )}{1 + 1 ^{2}}

Expand

\frac{1 \cdot cos ( x )}{1 + 1 ^{2}} : \frac{cos ( x )}{2}

= \frac{cos ( x )}{2}

\frac{d}{d θ} (y (θ)) + y (θ) = 0

y^{^{'}} = - 3 y, y (0) = e^{- 3 t}, y (0) = 1

\frac{d y}{d x} + ln (x) y = 3 ln (x)

y^{^{'}} = 2 y^{- 2}, y (0) = 3

(y + 2) d x + 25 - x^{2} d y = 0

What is the (dy)/(dx)=(ycos(x))/(1+y^2),y(0)=1 ?
The (dy)/(dx)=(ycos(x))/(1+y^2),y(0)=1 is (cos(x))/2