Answered: Use an appropriate substitution to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A Bernoulli differential equation is one of the form dydx+P(x)y=Q(x)yn.dydx+P(x)y=Q(x)yn. Observe that, if n=0n=0 or 11, the Bernoulli equation is linear. For other values of nn, the A Bernoulli differential equation is one of the form dydx+P(x)y=Q(x)yn.dydx+P(x)y=Q(x)yn. Observe that, if n=0n=0 or 11, the Bernoulli equation is linear. For other values of nn, the substitution u=y1−nu=y1−n transforms the Bernoulli equation into the linear equation dudx+(1−n)P(x)u=(1−n)Q(x).dudx+(1−n)P(x)u=(1−n)Q(x). Use an appropriate substitution to solve the equation y′−(5/x)y=y^4/x^10,y′−((5/x)y)=y^4/x^13, and find the solution that satisfies y(1)=1.y(1)=1.

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