AP EAMCET · Maths · Differential Equations
The differential equation for which \(y^2=4 a(x+a)\) (a is the parameter) is the general solution is
- A \(y=2 x \frac{d y}{d x}+y\left(\frac{d y}{d x}\right)^2\)
- B \(y=y \frac{d y}{d x}-x\left(\frac{d y}{d x}\right)^2\)
- C \(x=3 \frac{d y}{d x}+y\left(\frac{d y}{d x}\right)^2\)
- D \(y=3 x^2 \frac{d y}{d x}+y^2\left(\frac{d y}{d x}\right)^2\)
Answer & Solution
Correct Answer
(A) \(y=2 x \frac{d y}{d x}+y\left(\frac{d y}{d x}\right)^2\)
Step-by-step Solution
Detailed explanation
\(y^2=4 a(x+a)\) \(2y \frac{dy}{dx} = 4a\) \(a = \frac{1}{2} y \frac{dy}{dx}\) \(y^2 = 4 \left( \frac{1}{2} y \frac{dy}{dx} \right) \left( x + \frac{1}{2} y \frac{dy}{dx} \right)\) \(y = 2x \frac{dy}{dx} + y \left(\frac{dy}{dx}\right)^2\)
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