Q11 of 50 Page 193

If y(x) is a solution of and y(0) = 1, then find the value of

given:


To find: solution of the given differential equation


Re-writing the equation as



Integrating both sides




Let sin x=t


cos x dx=dt


formula:



Formula:


ln(1+y) = -ln(2+t)+log c


ln(1+y)+ln(2+sin x )=log c


(1+y)(2+sinx) = c



When x = 0 and y = 1




c = 4



If x = π/2 then,






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