Help to solve differentail equation

Mekhala

New member
Joined
Mar 20, 2021
Messages
3
eliminate the arbitrary constants a & b from z^2 =ax^3 +by^3+ab
 

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
7,535
So this is NOT "solving" a differential equation, it is creating a differential equation.

The derivative of a constant is 0 so start differentiating!

Differentiate with respect to x
\(\displaystyle 2z\frac{\partial z}{\partial x}= 3ax^2\)

Differentiate again with respect to y
\(\displaystyle 2z\frac{\partial^2z}{\partial x\partial y}+ 2\frac{\partial z}{\partial x}\frac{\partial z}{\partial y}= 0\)
 
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