Q120 / 160 · AP EAMCET 2022 (08 Jul Shift 1) · Mathematics

$y=a x+b$ is

  • A
    General solution of $\frac{d^3 y}{d x^3}=0$
  • B
    General solution for $\frac{d y}{d x}=a+b$
  • C
    General solution for both $\frac{d^2 y}{d x^2}=0$ and $\frac{d^3 y}{d x^3}=0$
  • Correct answer
    D
    General solution for $\frac{d^2 y}{d x^2}=0$

Solution

$y=a x+b$ $\begin{aligned} & \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{a} \\ & \frac{\mathrm{d}^2 \mathrm{y}}{\mathrm{dx}^2}=0\end{aligned}$ $\Rightarrow \mathrm{y}=\mathrm{ax}+\mathrm{b}$ is general solution of $\frac{\mathrm{d}^2 \mathrm{y}}{\mathrm{dx}^2}=0$

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

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