The solution curve of the differential equation, (1 + e⁻ˣ)(1 + y²)dy/dx = y², which passes through the point (0,1), is
The solution curve of the differential equation, (1 + e⁻ˣ)(1 + y²)dy/dx = y², which passes through the point (0,1), is
Option 1 -
y² + 1 = y(logₑ((1+eˣ)/2) + 2)
Option 2 -
y² + 1 = ylogₑ((1+e⁻ˣ)/2)
Option 3 -
y² + 1 = y(logₑ((1+e⁻ˣ)/2) + 2)
Option 4 -
y² = 1 + ylogₑ((1+e⁻ˣ)/2)
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:(1 + e? ) (1 + y²) dy/dx = y²
⇒ (1 + y? ²)dy = ( e? / (1 + e? ) ) dx
⇒ (y - 1/y) = ln (1 + e? ) + c
∴ It passes through (0,1) ⇒ c = -ln2
⇒ y² = 1 + yln ( (1+e? )/2 )
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