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Question: Answered & Verified by Expert
Observe the following statements
A. Integrating factor of $\frac{d y}{d x}+y=x^2$ is $e^x$
R. Integrating factor of $\frac{d y}{d x}+P(x) y=Q(x)$ is $e^{\int P(x) d x}$

Then, the true statement among the following is
MathematicsDifferential EquationsAP EAMCETAP EAMCET 2004
Options:
  • A $A$ is true, $R$ is false
  • B $A$ is false, $R$ is true
  • C $A$ is true, $R$ is true, $R \Rightarrow A$
  • D Both are false
Solution:
2134 Upvotes Verified Answer
The correct answer is: $A$ is true, $R$ is true, $R \Rightarrow A$
Statement A
Integrating factor of $\frac{d y}{d x}+y=x^2=e^{\int 1 \cdot d x}=e^x$
Statement R
$$
\begin{aligned}
\frac{d y}{d x}+P(x) y & =Q(x) \\
\operatorname{IF} & =e^{\int P(x) d x}
\end{aligned}
$$
$\therefore$ Both statements $A$ and $B$ are true and statement $\mathrm{R} \Rightarrow \mathrm{A}$.

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