eliminate the arbitrary constants a & b from z^2 =ax^3 +by^3+ab
M Mekhala New member Joined Mar 20, 2021 Messages 3 Mar 20, 2021 #1 eliminate the arbitrary constants a & b from z^2 =ax^3 +by^3+ab
H HallsofIvy Elite Member Joined Jan 27, 2012 Messages 7,763 Mar 22, 2021 #2 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 2z∂z∂x=3ax2\displaystyle 2z\frac{\partial z}{\partial x}= 3ax^22z∂x∂z=3ax2 Differentiate again with respect to y 2z∂2z∂x∂y+2∂z∂x∂z∂y=0\displaystyle 2z\frac{\partial^2z}{\partial x\partial y}+ 2\frac{\partial z}{\partial x}\frac{\partial z}{\partial y}= 02z∂x∂y∂2z+2∂x∂z∂y∂z=0
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 2z∂z∂x=3ax2\displaystyle 2z\frac{\partial z}{\partial x}= 3ax^22z∂x∂z=3ax2 Differentiate again with respect to y 2z∂2z∂x∂y+2∂z∂x∂z∂y=0\displaystyle 2z\frac{\partial^2z}{\partial x\partial y}+ 2\frac{\partial z}{\partial x}\frac{\partial z}{\partial y}= 02z∂x∂y∂2z+2∂x∂z∂y∂z=0
