and 3 others joined a min ago.
0
253views
$$ u=x^{3}+3 x^{2} y+3 x y^{2}+y^{3} \text {, prove that } x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}=3 u \text {. } $$
1 Answer
0
0views
written 2.1 years ago by
prajapatijaimin
• 3.1k
|
Solution:
$$ \begin{aligned} u &=x^{3}+3 x^{2} y+3 x y^{2}+y^{3}.....(A) \\\\ \frac{\partial u}{\partial x} &=3 x^{2}+6 x y+3 y^{2}+0 \\\\ x \frac{\partial u}{\partial x} &=x\left(3 x^{2}+6 x y+3 y^{2}\right) \\\\ x \frac{\partial u}{\partial x} &=3 x^{3}+6 x^{2} y+3 x y^{2}........(1) \\\\ u &=x^{3}+3 x^{2} y+3 x y^{2}+y^{3} \\\\ \frac{\partial u}{\partial y} …
and 2 others joined a min ago.
ADD COMMENT
EDIT
Please log in to add an answer.