Q119 / 160 · AP EAMCET 2019 (21 Apr Shift 1) · Mathematics

The differential equation of all parabolas whose axes are parallel to $Y$-axis is

  • Correct answer
    A
    $\frac{d^3 y}{d x^3}=0$
  • B
    $\frac{d^2 y}{d x^2}=0$
  • C
    $\frac{d^2 y}{d x^2}+\frac{d y}{d x}=0$
  • D
    $y \frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^2=0$

Solution

Let $y=A x^2+B x+C$ Differentiate w.r.t. $x$, we get $$ \frac{d y}{d x}=2 A x+B $$ Again, differentiate w.r.t. $x$, we get $$ \frac{d^2 y}{d x^2}=2 A $$ Again, differentiate w.r.t. $x$, we get $$ \frac{d^3 y}{d x^3}=0 $$ This is required equation.

Hence, the correct answer is option: 'A'.

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