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For differential equation (1-e^x)sec^2ydy+3e^xtanydx=0 If y(ln2)=pi/4 Then y(ln3) is equal to

For differential equation 
(1-e^x)sec^2ydy+3e^xtanydx=0
If y(ln2)=pi/4
Then y(ln3) is equal to

Grade:12

1 Answers

Aditya Gupta
2081 Points
5 years ago
first of all put tany=z which means dz=sec^2ydy so the eqn becomes
(1-e^x)dz/dx+3ze^x=0
or dz/z= 3e^xdx/(e^x – 1)
integrate both sides and plug in the initial conditions.
lnz+C=3ln(e^x – 1) 
you can calculate the final answer now

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