4 ms·
The real formal procedure: dy/dx = g(x)f(y) Let h(y) = 1/f(y) => dy/dx = g(x)/h(y) => h(y) dy/dx = g(x) Now, we integrate both sides, int h(y) dy/dx dx =
by d4rkn0d3z 11mo ago
The real formal procedure:
dy/dx = g(x)f(y)
Let h(y) = 1/f(y)
=> dy/dx = g(x)/h(y)
=> h(y) dy/dx = g(x)
Now, we integrate both sides,
int h(y) dy/dx dx = int g(x) dx
But the left hand side is the same as
int h(y) dy by substitution rule of integration.
Therefore,
int h(y) dy = int g(x) dx
Proceed with solving now, no abuse since the substitution rule is provable. QED