MCQ
The differential equation whose solution is $A{x^2} + B{y^2} = 1$ where $A$ and $B$ are arbitrary constants is of
- Asecond order and second degree
- Bfirst order and second degree
- Cfirst order and first degree
- ✓second order and first degree
$A x+b y \frac{d y}{d x}=0 \quad \ldots(2)$
$A+B y \frac{d^{2} y}{d x^{2}}+B\left(\frac{d y}{d x}\right)^{2}=0 \quad \ldots(3)$
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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$[A]$ $\mathrm{P}\left(\mathrm{X}^{\prime} \mid \mathrm{Y}\right)=\frac{1}{2}$ $[B]$ $\mathrm{P}(\mathrm{X} \cap \mathrm{Y})=\frac{1}{5}$ $[C]$ $\mathrm{P}(\mathrm{X} \cup \mathrm{Y})=\frac{2}{5}$ $[D]$ $\mathrm{P}(\mathrm{Y})=\frac{4}{15}$