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A Bernoulli differential equation is one of the form dxdy+P(x)y=Q(x)yn Observe that, if n=0 or 1,...

A Bernoulli differential equation is one of the form dxdy+P(x)y=Q(x)yn

Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y^(1−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'−(3/x)y=y^4/x^2 and find the solution that satisfies y(1)=1

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