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9. differential equations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths9. differential equations1 Mark
MCQ
The differential equation whose solution is $A{x^2} + B{y^2} = 1$ where $A$ and $B$ are arbitrary constants is of
  • A
    second order and second degree
  • B
    first order and second degree
  • C
    first order and first degree
  • ✓
    second order and first degree
✓

Answer

Correct option: D.
second order and first degree
d
$A x^{2}+B y^{2}=1 \quad \dots(1)$

$A x+b y \frac{d y}{d x}=0 \quad \ldots(2)$

$A+B y \frac{d^{2} y}{d x^{2}}+B\left(\frac{d y}{d x}\right)^{2}=0 \quad \ldots(3)$

From $(2)$ and $(3)$

$x\left\{-B y \frac{d^{2} y}{d x^{2}}-B\left(\frac{d y}{d x}\right)^{2}\right\}+B y \frac{d y}{d x}=0$

Dividing both sides by $-B,$ we get

$\Rightarrow x y \frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}=0$

Which is $D E$ of order $2$ and degree $1$

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