A first order equation $\frac{dy}{dx} = f \left( x,y \right)$ is said to be a Bernoulli equation if f(x,y) is of the form $g \left( x \right) y + h \left( x \right) y^{a}$.

**Steps to solve $f \left( x,y \right) = g \left( x \right) y + h \left( x \right) y^{a}$:**

**1) Divide by y ^{a} to get $y^{-a} \frac{dy}{dx} = g \left( x \right) y^{1-a} + h \left( x \right)$**

**2) Multiply by (1 – a) to get $\left( 1-a \right) y^{-a} \frac{dy}{dx} = \left( 1-a \right) g \left( x \right) y^{1-a} + \left( 1-a \right) h \left( x \right)$**

**3) Let z = y ^{(1 – a)} so that equation becomes:**

**$$ \frac{dz}{dx} = (1 – a)g(x)z + (1 – a)h(x)$$**

**4) Solve this linear differential equation for z.**

**5) Substitute back y ^{(1 – a)} = z**

**6) Solve the implicit solution for y.**