Solve the differential equation:
(1-2x^2-2y)dy/dx=4x^3+4xy

Step-by-step explanation:

We are given that

We have to solve the given differential equation

Compare with

Then, we get

Exact differential equation

Hence, the differential equation is an exact differential equation.

Solution of exact differential is given by

where K(y) is a function of y.

y treated as constant

Substitute the value then we get

Then,

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: