Q118 / 160 · TS EAMCET 2020 (10 Sep Shift 2) · Mathematics

The differential equation for which $y=a x^2+b x+c$ is the general solution is

  • A
    $\frac{d^4 y}{d x^4}=0$
  • Correct answer
    B
    $\frac{d^3 y}{d x^3}=0$
  • C
    $\frac{d^5 y}{d x^5}=0$
  • D
    $\frac{d^3 y}{d x^3}+\frac{d^4 y}{d x^4}=0$

Solution

We have, $y=a x^2+b x+c$ Here, Number of arbitrary constants are three as $a, b$ and $c$ On differentiating both sides w.r.t.' $x^{\prime} \frac{d y}{d x}=2 a x+b$ Again, $\frac{d^2 y}{d x^2}=2 a$ Again, differentiate, w.r.t. ' $x$ ' $\frac{d^3 y}{d x^3}=0$

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

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