SOLUTION: A Bernoulli differential equation is one of the form dy/dx+P(x)y=Q(x)y^n. Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution

Question 1184077: A Bernoulli differential equation is one of the form
dy/dx+P(x)y=Q(x)y^n.
Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y1−n transforms the Bernoulli equation into the linear equation
du/dx+(1−n)P(x)u=(1−n)Q(x).
Use an appropriate substitution to solve the equation
y′−(7/x)y=(y^4/x^5), and find the solution that satisfies y(1)=1.
y(x)= ?
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Let . Substituting this into the original D.E. and simplifying, you get

.

The integrating factor is .
After multiplying D.E. with the integrating factor and integrating,
you get

. ===> , or .

solving for C when y(1) = 1 gives , so that

.

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