TS EAMCET · Maths · Differential Equations
A family of curves whose equation is general solution of a differential equation having order 1 and degree 3 , is \((g, a, c\) are arbitrary constants)
- A \(x^2+y^2+2 g x+4 y+2=0\)
- B \(x^2=a^2\left(1+y^2\right)\)
- C \(y^2=2 c(x+\sqrt{c})\)
- D \(y^2=4 a x\)
Answer & Solution
Correct Answer
(C) \(y^2=2 c(x+\sqrt{c})\)
Step-by-step Solution
Detailed explanation
On solving by options, we get (a) \(x^2+y^2+2 g x+4 y+2=0\) \[ \Rightarrow 2 x+2 y \frac{d y}{d x}+2 g+4 \frac{d y}{d x}=0 \] [differentiating both sides w.r.t. ' \(x\) '] \[ \Rightarrow \quad-\left(x+y \frac{d y}{d x}+2 \frac{d y}{d x}\right)=g \] On substituting value of \(g\)…
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