Solution of the differential equation cosxdy=y(sinx-y)dx ,0 x /2 - Maths - Differential Equations

Question

Solution of the differential equation cosxdy=y(sinx-y)dx
,0<x<π/2

Priyanka Kedia · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

We have, cosx dy=ysinx-ydx⇒dydx=y tanx-y2secx⇒1y2dydx-1ytanx=-secx        
1Let 1y=t⇒-1y2dydx=dtdx, so equation 1 becomes,-dtdx-t tanx=-secx⇒dtdx+t tanx=secxNow,I
F =e∫tanx dx=elogsecx=secxSo,t×I F
=∫secx×I F
 dx⇒t secx=∫sec2xdx⇒t secx=tanx +C⇒1y secx=tanx +C⇒secx=ytanx +C

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Solution of the differential equation cosxdy=y(sinx-y)dx ,0<x<π/2