For the differential equation frac{d^3 y}{d x | vedclass

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(A) The given differential equation is $\frac{d^3 y}{d x^3} = 0$. Integrating both sides with respect to $x$ three times: First integration: $\frac{d^

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the general solution

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(A) The given differential equation is $\frac{d^3 y}{d x^3} = 0$. Integrating both sides with respect to $x$ three times: First integration: $\frac{d^2 y}{d x^2} = c_1$. Second integration: $\frac{d y}{d x} = c_1 x + c_2$. Third integration: $y = \frac{c_1}{2} x^2 + c_2 x + c_3$. Letting $a = \frac{c_1}{2}$,$b = c_2$,and $c = c_3$,we get $y = a x^2 + b x + c$. Since this solution contains three arbitrary constants $(a, b, c)$ equal to the order of the differential equation,it is the general solution. Thus,the correct option is $A$.

For the differential equation $\frac{d^3 y}{d x^3}=0$,$y=a x^2+b x+c$ is

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