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Question : 78 of 160
Marks:
+1,
-0
Solution:
‌+ycosec2x=cosec2x⋅cot‌x We have,
{‌+Py=Q then,
IF=e∫Pdx} Solution is
y(IF)=∫Q(IF)dx+6 Here,
P=cosec2x,Q=cosec2x⋅cot‌x IF=e∫Pdx=e∫cosec2xdx⇒IF=e−cos‌x Solution is
y(IF)=∫Q(IF)dx+c ye−cot‌x=∫(cosec2x⋅cot‌x)⋅e−cot‌xdx+c Put
−cot‌x=t cosecxdx‌‌=dt y⋅e−cot‌x‌‌=∫−te′dt+c ye−cot‌x‌‌=−∫t⋅etdt+c ye−cot‌x‌‌=−(t−1)et+c ye−cot‌x‌‌=−(−cot‌x−1)e−cot‌x+c ye−cot‌x‌‌=(cot‌x+1)⋅e−cot‌x+c
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