Question

50 points each question. Please help. How do I solve?

Answer 1

`~~~~~7e^(xy) +2x^2 -4y^2 =13\\\\\\\implies (d)/(dx)\left(7e^(xy) +2x^2 -4y^2\right) =\frac d{dx} (13)\\\\\\\implies 7\left[e^(xy) (d)/(dx) ( xy)\right] +2 \cdot 2x -4\cdot 2y (dy)/(dx) = 0\\\\\\\implies 7e^(xy) \left( x (dy)/(dx) +y\right) +4x -8y (dy)/(dx) =0\\\\\\\implies 7xe^(xy)(dy)/(dx) + 7ye^(xy) +4x -8y(dy)/(dx) = 0\\\\\\\implies \left(7xe^(xy) -8y \right) (dy)/(dx)=-7ye^(xy) -4x\\\\\\`

`\implies (dy)/(dx) = (-7ye^(xy) -4x)/(7xe^(xy) -8y )`