Observe the following statements:A. Integrati | vedclass

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(C) For statement $A$: The given differential equation is $\frac{dy}{dx} + y = x^2$. Comparing this with the standard form $\frac{dy}{dx} + P(x)y = Q(

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$A$ is true,$R$ is true,$R \Rightarrow A$

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(C) For statement $A$: The given differential equation is $\frac{dy}{dx} + y = x^2$. Comparing this with the standard form $\frac{dy}{dx} + P(x)y = Q(x)$,we get $P(x) = 1$. The integrating factor $(IF)$ is $e^{\int P(x) dx} = e^{\int 1 dx} = e^x$. Thus,statement $A$ is true.For statement $R$: The standard form of a linear differential equation is $\frac{dy}{dx} + P(x)y = Q(x)$,and its integrating factor is defined as $e^{\int P(x) dx}$. Thus,statement $R$ is true.Since statement $A$ is derived directly from the definition provided in statement $R$,$R \Rightarrow A$ is true.

Observe the following statements:
$A$. Integrating factor of $\frac{dy}{dx} + y = x^2$ is $e^x$.
$R$. Integrating factor of $\frac{dy}{dx} + P(x)y = Q(x)$ is $e^{\int P(x) dx}$.
Then,the true statement among the following is:

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Observe the following statements:$A$. Integrating factor of $\frac{dy}{dx} + y = x^2$ is $e^x$.$R$. Integrating factor of $\frac{dy}{dx} + P(x)y = Q(x)$ is $e^{\int P(x) dx}$.Then,the true statement among the following is: