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SOLVED:A Bernoulli differential equation (named after James Bernoulli) is of the form (d y)/(d x)+P(x) y=Q(x) y^n Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n , show that the substitution u=y^1-n transforms the Bernoulli equation into the linear equation (d u)/(d x)+(1-n) P(x) u=(1-n) Q(x)

SOLVED:A Bernoulli differential equation (named after James Bernoulli) is of the form (d y)/(d x)+P(x) y=Q(x) y^n Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n , show that the substitution u=y^1-n transforms the Bernoulli equation into the linear equation (d u)/(d x)+(1-n) P(x) u=(1-n) Q(x)

2020年5月12日

A Bernoulli differential equation (named after James Bernoulli) is 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, show that 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) | Numerade

A Bernoulli differential equation (named after James Bernoulli) is 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, show that 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) | Numerade

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