JEE Mains · Maths · STD 12 - 9. differential equations
If for \(x \geq 0, y=y(x)\) is the solution of the differential equation \((\mathrm{x}+1) \mathrm{d} \mathrm{y}=\left((\mathrm{x}+1)^{2}+\mathrm{y}-3\right) \mathrm{d} \mathrm{x}, \mathrm{y}(2)=0\) then \(y(3)\) is equal to
- A \(9\)
- B \(1\)
- C \(7\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\((\mathrm{x}+1) \mathrm{d} \mathrm{y}-\mathrm{ydx}=\left((\mathrm{x}+1)^{2}-3\right) \mathrm{d} \mathrm{x}\) \(\Rightarrow \quad \frac{(\mathrm{x}+1) \mathrm{d} \mathrm{y}-\mathrm{ydx}}{(\mathrm{x}+1)^{2}}=\left(1-\frac{3}{(\mathrm{x}+1)^{2}}\right) \mathrm{dx}\)…
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