AP EAMCET · Maths · Differential Equations
If \(c\) is a parameter, then the differential equation of the family of curves \(x^2=c(y+c)^2\) is
- A \(x\left(\frac{d y}{d x}\right)^3+y\left(\frac{d y}{d x}\right)^2-1=0\)
- B \(x\left(\frac{d y}{d x}\right)^3-y\left(\frac{d y}{d x}\right)^2+1=0\)
- C \(x\left(\frac{d y}{d x}\right)^3+y\left(\frac{d y}{d x}\right)^2+1=0\)
- D \(x\left(\frac{d y}{d x}\right)^3-y\left(\frac{d y}{d x}\right)^2-1=0\)
Answer & Solution
Correct Answer
(D) \(x\left(\frac{d y}{d x}\right)^3-y\left(\frac{d y}{d x}\right)^2-1=0\)
Step-by-step Solution
Detailed explanation
Given equation of the family of curves \(\begin{aligned} & x^2=c(y+c)^2 \\ & x=\sqrt{c}(y+c) \quad \ldots (i) \end{aligned}\) [on taking square root both sides] Now, differentiate both sides w.r.t. \(x\), we get…
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