ExamBro
ExamBro
TS EAMCET · Maths · Differential Equations

\(f\left(x, y, c_1, c_2\right)=0\) is an equation containing two arbitrar constants \(c_1\) and \(c_2\). If the differential equation havin \(f\left(x, y, c_1, c_2\right)=0\) as its general solution is of \(k^{\text {th }}\) order, the the differential equation corresponding to \(x^k+y^k=c^2\) ( \(c\) is an arbitrary constant) is

  1. A \(\frac{d y}{d x}+\frac{x}{y}=0\)
  2. B \(\frac{d y}{d x}+\frac{y}{x}=0\)
  3. C \(\frac{d y}{d x}-\frac{x}{y}=0\)
  4. D \(\frac{d y}{d x}-\frac{y}{x}=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{d y}{d x}+\frac{x}{y}=0\)

Step-by-step Solution

Detailed explanation

Since the given equation \(\mathrm{x}^{\mathrm{k}}+\mathrm{y}^{\mathrm{k}}=\mathrm{c}^2\) has two arbitrary constants \(\mathrm{C}_1, \mathrm{C}_2\) hence \(\mathrm{k}=2\)…