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Solve ytanx dy/dx=(4+y^2)sec^2x please i need help on this question asap

Solve ytanx dy/dx=(4+y^2)sec^2x please i need help on this question asap

Grade:6

1 Answers

Arun
25750 Points
6 years ago
Dear student
 
y dy/(4+y²) = sec²x dx/tanx
On integrating
In LHS
4+ y² = t (assume)
2y dy = dt
y dy = dt/2
Now LHS
dt/2t = (1/2) ln t = (1/2) ln(4+y²)
 
Now for RHS
Put tanx = z (assume)
Sec²x dx = dz
Hence
dz/z = ln z = ln (tanx)
 
Hence final answer will be
(1/2) ln(4+y²) = ln (tanx) + C
 
Regards
Arun (AskIITians forum expert)

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