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HW 2.4: Problem 3 Previous Problem Problem List Next Problem (1 point) A Bernoulli differential equation is one of the form + P(x)y -- Q(x)y". Observe that, if n = 0 or 1, the Bemoulli equation is linear. For other values of n the substitution -y transforms the Bernoulli equation into the linear equation + (1 - n)P(x)u = (1 - 1)(a). Use an appropriate substitution to solve the equation and find the solution that satisfies y(1) = 1. Preview My Answers Submit Answers

Answer 1

H 24 Problem 3 A Benoulli diffexeutial ogh is of tue Pdrm me P) ) + Obsewe hat , f- n=o r 1, +he Bernoulli eq" is Uneosu . tramsfer m of substitution the tue Bernoulli -eq^ into the kino an ean du (1-h)P) u = (-)gcx). SolutionPut -h lroue Diff. 'u' w. x.Ho ue du h have Putthg vnlues of , in e P) uy dx Frm 4 + dx multipgmy balh sidus tq 4 Ho franformed eq form Bernouli eqv in in can Use ta oppropviate stdasHitution to sohe the 6 We Aubstitute. 6o Hhat 5 ch Ly5 du 4 dx
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Putriny we haue frem 4the values of dx Multiphy both Aides b- du do Thio in ordinany ditfrential eq", S da Tutegratin factor(1.) e The general &0l" where Gin arbt Contuit 4 16 16 10 dx 4 4 11 -.৭-ह x5 4 1 11 Hence 4 15 10 4 x 15 x-16 equired soof eq" This io tue
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