JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{ dy }{ dx }+\left(\frac{2 x ^{2}+11 x +13}{ x ^{3}+6 x ^{2}+11 x +6}\right)\) \(y=\frac{(x+3)}{x+1}, x>-1\), which passes through the point \((0,1)\). Then \(y (1)\) is equal to.
- A \(\frac{1}{2}\)
- B \(\frac{3}{2}\)
- C \(\frac{5}{2}\)
- D \(\frac{7}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}+\left(\frac{2 x^{2}+11 x+13}{x^{3}+6 x^{2}+11 x+6}\right) y=\frac{x+3}{x+1}\) \(\int p(x) d x \quad \text { I.F. }=e^{\int p(x) d x}\) \(\int p(x) d x=\int \frac{\left(2 x^{2}+11 x+13\right) d x}{(x+1)(x+2)(x+3)}\)Using partial fraction…
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