Find the solution to the given differential equation

[chwala]

Homework Statement

see attached

Relevant Equations

ode/pde

I need insight on the highlighted in Red on how $\left[\dfrac{dz}{dx} - 1 = \dfrac{dy}{dx}\right]$ otherwise the rest of the steps are clear. I just read that $\dfrac{dx}{dy} \dfrac{dy}{dz} \dfrac{dz}{dx} =-1$

 

[renormalize]

I need insight on the highlighted in Red on how $\left[\dfrac{dz}{dx} - 1 = \dfrac{dy}{dx}\right]$ otherwise the rest of the steps are clear.

Just differentiate $z=x+y$ with respect to $x$.

 

[chwala]

Just differentiate $z=x+y$ with respect to $x$.

I thought of that- the confusion was on what to do with $\dfrac{dz}{dy}$. Thks.

 

[renormalize]

I thought of that- the confusion was on what to do with $\dfrac{dz}{dy}$. Thks.

The derivative $dz/dy$ doesn't appear in the equation you're trying to derive, so don't worry about it.

 

[chwala]

Just differentiate $z=x+y$ with respect to $x$.

Thanks man!!! i was blind.

$z=x+y$

$\dfrac{dz}{dx} = 1 + \dfrac{dy}{dx}$

$\dfrac{dz}{dx} -1 = \dfrac{dy}{dx}$