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24-10-2020
Mathematics

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Solve the initial-value problem y' = (8 sin(x))/sin(y), y(0) = pi/2

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evgeniylevi evgeniylevi

26-10-2020

Answer:

8cosx-cosy=8.

Step-by-step explanation:

dy/dx=8sinx/siny;

sinydy=8sinxdx;

-cosy= -8cosx+C;

according to the condition y(0)=pi/2:

-cos(pi/2)= -8cos0+C;

-8+C=0; ⇔ C=8, then

8cosx-cosy=8.

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