JEE Mains · Maths · STD 12 - 9. differential equations
The differential equation satisfied by the system of parabolas \(y ^{2}=4 a ( x + a )\) is
- A \(y\left(\frac{d y}{d x}\right)^{2}-2 x\left(\frac{d y}{d x}\right)-y=0\)
- B \(y\left(\frac{d y}{d x}\right)^{2}-2 x\left(\frac{d y}{d x}\right)+y=0\)
- C \(y\left(\frac{d y}{d x}\right)^{2}+2 x\left(\frac{d y}{d x}\right)-y=0\)
- D \(y\left(\frac{d y}{d x}\right)+2 x\left(\frac{d y}{d x}\right)-y=0\)
Answer & Solution
Correct Answer
(C) \(y\left(\frac{d y}{d x}\right)^{2}+2 x\left(\frac{d y}{d x}\right)-y=0\)
Step-by-step Solution
Detailed explanation
\(y ^{2}=4 ax +4 a ^{2}\) differentiate with respect to \(x\) \(\Rightarrow 2 y \frac{ dy }{ dx }=4 a\) \(\Rightarrow a =\left(\frac{ y }{2} \frac{ dy }{ dx }\right)\) so, required differential equation is…
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