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Popular >

(sin(θ))(dy)/(dθ)=cos(θ)

Solution

(sin (θ)) \frac{d y}{d θ} = cos (θ)

Solution

y (θ) = ln (sin (θ)) + c_{1}

Solution steps

(sin (θ)) \frac{d y}{d θ} = cos (θ)

Substitute

\frac{d y}{d θ}

with

y^{'} (θ)

(sin (θ)) y^{^{'}} (θ) = cos (θ)

Isolate

y^{'} (θ) : y^{'} (θ) = \frac{cos ( θ )}{sin ( θ )}

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y (θ) = \int \frac{cos ( θ )}{sin ( θ )} d θ

\int \frac{cos ( θ )}{sin ( θ )} d θ = ln (sin (θ)) + c_{1}

y (θ) = ln (sin (θ)) + c_{1}

Popular Examples

integral of (x^3-1)e^{-x/3}

\int (x^{3} - 1) e^{- \frac{x}{3}} d x

derivative of-(120/(x^6))

\frac{d}{d x} (- \frac{120}{x ^{6}})

\frac{d}{d z} (x y)

x^3y^'+2x^2y=-4cos(2x)y^{-1/2}

x^{3} y^{^{'}} + 2 x^{2} y = - 4 cos (2 x) y^{- \frac{1}{2}}

limit as x approaches 1 of 5/(x^3-1)

x \to 1 lim (\frac{5}{x ^{3} - 1})

Frequently Asked Questions (FAQ)

What is the solution for (sin(θ))(dy)/(dθ)=cos(θ) ?
The solution for (sin(θ))(dy)/(dθ)=cos(θ) is y(θ)=ln(sin(θ))+c_{1}