Solve y=|y|*sinx - ScanMath

Calculate

y = ∣ y ∣ \cdot sin (x)

Take the derivative of both sides

\frac{d}{d x} (y) = \frac{d}{d x} (∣ y ∣ \times sin (x))

Calculate the derivative

More Steps

\frac{d y}{d x} = \frac{d}{d x} (∣ y ∣ \times sin (x))

Calculate the derivative

More Steps

\frac{d y}{d x} = \frac{y \frac{d y}{d x} \times sin ( x )}{∣ y ∣} + ∣ y ∣ \times cos (x)

Rewrite the expression

\frac{d y}{d x} = \frac{y sin ( x ) \frac{d y}{d x}}{∣ y ∣} + ∣ y ∣ \times cos (x)

Multiply both sides of the equation by LCD

\frac{d y}{d x} ∣ y ∣ = (\frac{y sin ( x ) \frac{d y}{d x}}{∣ y ∣} + ∣ y ∣ \times cos (x)) ∣ y ∣

Simplify the equation

∣ y ∣ \times \frac{d y}{d x} = (\frac{y sin ( x ) \frac{d y}{d x}}{∣ y ∣} + ∣ y ∣ \times cos (x)) ∣ y ∣

Simplify the equation

More Steps

∣ y ∣ \times \frac{d y}{d x} = y sin (x) \frac{d y}{d x} + y^{2} cos (x)

Move the variable to the left side

∣ y ∣ \times \frac{d y}{d x} - y sin (x) \frac{d y}{d x} = y^{2} cos (x)

Collect like terms by calculating the sum or difference of their coefficients

(∣ y ∣ - y sin (x)) \frac{d y}{d x} = y^{2} cos (x)

Divide both sides

\frac{( ∣ y ∣ - y sin ( x ) ) \frac{d y}{d x}}{∣ y ∣ - y sin ( x )} = \frac{y ^{2} cos ( x )}{∣ y ∣ - y sin ( x )}

Solution

\frac{d y}{d x} = \frac{y ^{2} cos ( x )}{∣ y ∣ - y sin ( x )}

Solve the equation