can someone help me with this please?

Write out grad u in terms of partial derivatives of u. Equate that to A. This gives three differential equations you can solve.

is that cross product what the hell is this notation

>>9019163
First you have to make sure that the rotation of A is 0 so
a = 3
b = 1
c = 0
then it becomes simple integration:
U = 2 x^2 + xy + 3xz - y^2 + z^2 + C

File: WP_20170707_15_48_29_Pro.jpg (886KB, 2592x1456px) Image search: [Google]

886KB, 2592x1456px

>>9019167
like this?

>>9019163

dU/dx = 4x+y+az
dU/dy = bx-2y
dU/dz = 3x+cy+2z

U = 2x^2 - y^2 + z^2 + axz + bxy + cxz + constant
a = 3
b = 1
c = 0

so U = 2x^2 - y^2 + z^2 + xy + 3xz + constant

>>9019191
how did you get the
> + axz + bxy + cxz
part?

>>9019195

dU/dx = ... + az so U has an axz term
dU/dy = ... + bx so U has a bxy term
dU/dz = ... + cy so U has a cxz term

think about how to calculate the values of a, b, c from here

>>9019202
oh ok ok thx

I think you calculate a,b,c from d>>9019182

>>9019207

yeah, one way is to notice that U_xz = U_zx
since dU/dx = 4x+y+az, d(dU/dx)/dz = a
and dU/dz = 3x+cy+2z, d(dU/dz)/dx = 3
so a = 3 and the other two follow similarly

File: WP_20170707_16_45_26_Pro.jpg (874KB, 1456x2592px) Image search: [Google]

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>>9019213
ok but one thing, I've integrated three equations to get three U equations, and then how do I get the final U?
what happened with circled numbers

>>9019286
bump

>>9019286
You integrated wrong. If
[eqn]\dfrac{\partial U}{\partial x} = 4x + y + az[/eqn]
then
[eqn] U = 2 x^2 + xy + axz + f(y,z) [/eqn]
with an unknown function [math] f [/math].

You can now use [math]\dfrac{\partial U}{\partial y} [/math] and [math]\dfrac{\partial U}{\partial z} [/math] to find [math] f [/math].

>>9019367
omg how much work is behind this is seem simple but it's not, I have no idea what that f is

>>9019371
[eqn] bx - 2y = \dfrac{\partial U}{\partial y} = x + \dfrac{\partial f}{\partial y}(y,z) [/eqn]
[eqn] f(y,z) = - y^2 + g(z) [/eqn]
[eqn] 3x + cy + 2z = \dfrac{\partial U}{\partial z} = ax + g'(z) [/eqn]
[eqn] g(z) = z^2 + C[/eqn]

This is all simple shit.

>>9019381
thanks for effort man but I have no idea what is going on here

>>9020097
oh fuck nice handwriting. would smash