A Bernoulli differential equation (named after James Bernoulli) is of the form dxdy​+P(x)y=Q(x)yn. Observe that, if n=0

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A Bernoulli Differential Equation Named After James Bernoulli Is Of The Form Dxdy P X Y Q X Yn Observe That If N 0 1 (25.2 KiB) Viewed 34 times

A Bernoulli differential equation (named after James Bernoulli) is 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=y1−n transforms the Bernoulli equation into the linear equation dxdu​+(1−n)P(x)u=(1−n)Q(x). Use the substitution u=y1−n to solve the differential equation. y′+x2​y=8x2y3​