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प्रश्न
Find the particular solution of the differential equation `dy/dx = y cot 2x`, given that `y(pi/4) = 2.`
योग
उत्तर
`dy/dx = ycot2x`
Given y = 2, x = `pi/4`
⇒ `dy/y = cot2x dx`
⇒ `intdy/y = intcot2x dx`
⇒ `log y = 1/2 log |sin 2x| + log C`
⇒ `log 4/sqrt (sin 2x) = log C`
⇒ `y/sqrt(sin^2x) = C` ...(i)
Put `x=pi/4, y=2` in eq (i)
⇒ C = 2
Hence `[y= 2sqrt(sin2x)]`
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