# Math Help - differential equation madness!

differential equation (dy/dx) = sin(y - x) is given show that if a new variable is defined by y = z^(1-n) then the equation (dz/dx) + p(x)z = q(x)z^n becomes a linear differential equation in y(x)

2. Then just do it.

We have $\frac{dz}{dx}\cdot \frac{1}{{{z}^{n}}}+\frac{p(x)}{{{z}^{n-1}}}=q(x)$ which is a Bernoulli ODE so put $y=\frac1{z^{n-1}}=z^{1-n}$ (and note that this is the suggested substitution) and you'll turn that ODE into a linear one.

3. i was given this and not taught Bernoulli's method, i read about it just now, it makes sense now, but isn't there another easier way to figure this out assuming you have no knowledge of bernoulli's equations and integrals (whatever there called)

4. Actually, in your problem was never told about Bernoulli's ODE; by following the substitution suggested, you must conclude that you'll get a linear ODE.

I just said that it is a Bernoulli's ODE since that's the way it's called, but nothing else.