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JEE Mains · Maths · STD 12 - 9. differential equations
The equation of the curve passing through the origin and satisfying the differential equation \(\left( {1 + {x^2}} \right)\,\frac{{dy}}{{dx}} + 2xy = 4{x^2}\) is
- A \((1 +x^2)\,y = x^3\)
- B \(3(1 + x^2 )\,y = 2x^3\)
- C \((1 +x^2)\,y = 3x^3\)
- D \(3(1 + x^2 )\,y = 4x^3\)
Answer & Solution
Correct Answer
(D) \(3(1 + x^2 )\,y = 4x^3\)
Step-by-step Solution
Detailed explanation
Given differential equation is \(\left(1+x^{2}\right) \frac{d y}{d x}+2 x y=4 x^{2}\) \(\Rightarrow \frac{d y}{d x}+\left(\frac{2 x}{1+x^{2}}\right) y=\frac{4 x^{2}}{1+x^{2}}\) This is linear diff. equation I.F…
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