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the differential equation (dy/dx)+p(x)y=Q(x) yn is

Mahesh Jat 8th Jun, 2021

Answer (1)

Aditi More 27th Jun, 2021

Hey,

An equation of the form dxdy+Py=Qun where P and Qare functions ofx alone or constants, is called Bernoulli's equation. Divide both the sides by yn, we get
y−ndxdy+Py−n+1=Q Put
y−n+1=z⇒(−n+1)y−ndxdy=dxdz.
The equation reduces to 1−n1dxdz+Pz=Q⇒dxdz+(1−n)Pz=Q
Which is linear in z and can be solved in the usual manner.
So the substitution is z=v=yn−11

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