Solving Linear Differential Equations of First Order
For the diffe...
Question
For the differential equation secxdydx=y+sinx. The solution is y=−(sinx+A)+cesinx. Find A
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Solution
secxdydx=y+sinx⇒dydx−ycosx=sinxcosx ...(1) Here P=cosx⇒∫Pdx=∫cosxdx=−sinx ∴I.F=e−sinx Multiplying (1) by I.F, we get e−sinxdydx−ycosxe−sinx=sinxcosxe−sinx Integrating both sides we get e−sinxy=e−sinx(−sinx−1)+c ⇒y=−(sinx+1)+cesinx