dy/dx = xe^(y-2x) , i am asked to form differential equation using this equation . the ans given is (e^-y) = 0.5(e^-2x)(x+0.5) + a , how to get the answer?
Solution:
Given: dy/dx = xe(y-2x)
dy/dx = x(ey/e2x)
We can arrange it as:
dy/ey= (x /e2x)dx
On integrating both the sides, we get;
∫(x /e2x)dx = ∫(dy/ey)
∫(x e-2x)dx = ∫(dy/ey)
On solving we will get;
e-y = 1/2 e-2x (x+1/2) +A