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BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Mathematics
Chapter
Differential Equations

BITSAT 2012 · Mathematics · Differential Equations

The differential equation whose solution is A x^ 2 +B y^ 2 =1 where...

The differential equation whose solution is Ax2+By2=1A x^{2}+B y^{2}=1 where AA and BB are arbitrary constants is of

Options

  1. Asecond order and second degree
  2. Bfirst order and second degree
  3. Cfirst order and first degree
  4. Dsecond order and first degree

Correct answer

D. second order and first degree

Step-by-step solution

Ax2+By2=1A x^{2}+B y^{2}=1...(1) Ax+Bydydx=0A x+B y \frac{d y}{d x}=0...(2) A+Byd2ydx2+B(dydx)2=0A+B y \frac{d^{2} y}{d x^{2}}+B\left(\frac{d y}{d x}\right)^{2}=0...(3) x{−Byd2ydx2−B(dydx)2}+Bydydx=0x\left\{-B y \frac{d^{2} y}{d x^{2}}-B\left(\frac{d y}{d x}\right)^{2}\right\}+B y \frac{d y}{d x}=0 Dividing both sides by −B-\mathrm{B}, we get xyd2ydx2+x(dydx)2−ydydx=0x y \frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}=0 Which is a DE of order 2 and degree 1
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