Differential Equations 2 Question 22

23. If y(x) satisfies the differential equation yytanx=2xsecx and y(0), then

(2012)

(a) yπ4=π282

(b) yπ4=π218

(c) yπ3=π29

(d) yπ3=4π3+2π233

(2016 Adv.)

Analytical & Descriptive Question

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Answer:

Correct Answer: 23. (a, d)

Solution:

  1. PLAN Linear differential equation under one variable.

dydx+Py=Q;IF=ePdx Solution is, y(IF)=Q(IF)dx+Cyytanx=2xsecx and y(0)=0dydxytanx=2xsecxIF=etanxdx=elog|cosx|=cosx

Solution is ycosx=2xsecxcosxdx+C

ycosx=x2+C As y(0)=0C=0y=x2secx Now, yπ4=π282yπ4=π2+π282yπ3=2π29yπ3=4π3+2π233



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