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    so i came across a differential equation and in order to solve it i had to integrate sinx cosx , i integrated using standard patterns and got (sin(x)^2)/2 +c , however in the solution bank they got (-1/4(cos(2x))) + c , i understand that these two solutions differ by some constant, but for my differential equation will it matter which form i put. Moreover, what happens if you evaluate this integral, you have more than one possible answer than give different solutions when evaluated (the constants cancel out?)
    the differential equation was
    cos y*sin2x*(dy/dx) = cot x cosec y
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    (Original post by Futurechemist)
    so i came across a differential equation and in order to solve it i had to integrate sinx cosx , i integrated using standard patterns and got (sin(x)^2)/2 +c , however in the solution bank they got (-1/4(cos(2x))) + c , i understand that these two solutions differ by some constant, but for my differential equation will it matter which form i put. Moreover, what happens if you evaluate this integral, you have more than one possible answer than give different solutions when evaluated (the constants cancel out?)
    the differential equation was
    cos y*sin2x*(dy/dx) = cot x cosec y
    Either answer is fine, since as you said, they differ by a constant. Even if you have conditions to apply, as long as everything is done correctly and consistently, any answer is correct as they all would produce the same curve.
 
 
 
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