Solve dy/dx+y/x=y² by bernollies equation ?
2 Answers
The general solution is
Explanation:
The Bernouilli ODE is of the form
The general solution is obtained by substituting
and solving
Here,
The equation is
Divide both sides by
Let
Differentiating both side wrt
Substituting in
The integrating factor is
Multiply
Integrating both sides
Substituting back
Explanation:
Bernoulli General Form:
#y'+P(x)y=Q(x)y^n qquad "with "{(P = 1/x),(Q = 1),(n = 2):}#
Standard substitution:
#z(x) = y^(1-n) = 1/y qquad :. z' = -1/y^2 y' #
So the DE
This is now linear, and can be solved by Integration factor:
#exp (int -1/x dx) = 1/x#