JEE Mains · Maths · STD 12 - 9. differential equations
If \(y=y(x)\) is the solution of the differential equation \(\frac{5+ e ^{ x }}{2+ y } \cdot \frac{ dy }{ dx }+ e ^{ x }=0\) satisfying \(y (0)=1,\) then a value of \(y \left(\log _{ e } 13\right)\) is
- A \(1\)
- B \(-1\)
- C \(2\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(-1\)
Step-by-step Solution
Detailed explanation
\(\frac{\left(5+ e ^{ x }\right)}{2+ y } \frac{ d y }{ dx }=- e ^{ x }\) \(\int \frac{ dy }{2+ y }=\int \frac{- e ^{ x }}{ e ^{ x }+5} dx\) \(\ln ( y +2)=-\ln \left( e ^{ x }+5\right)+ k\) \(( y +2)\left( e ^{ x }+5\right)= C\) \(\because y (0)=1\) \(\Rightarrow C =18\)…
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