AP EAMCET · Maths · Differential Equations
By multiplying with \(e^{\int P d x}\) on both sides of the equation \(\frac{d y}{d x}+P(x) y=Q(x)\), the left side of the equation takes the form \(\frac{d}{d x}(y f(x))\), then \(f(x)=\)
- A \(\int y e^{\int P d x} d x\)
- B y P(x)
- C \(e^{\int P d x}\)
- D \(\mathrm{P}(\mathrm{x}) e^{\int P d x}\)
Answer & Solution
Correct Answer
(C) \(e^{\int P d x}\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x}+P(x) y=Q(x)\) multiplying \(e^{\int P d x}\) on both sides of eqn. \(e^{\int P d x}\) \(\frac{d y}{d x}+y\) \(e^{\int P d x} P(x)\) \(=Q(x) e^{\int P d x}\) equating LHS with \(\frac{d}{d x}(y(f(x)))\) \(\Rightarrow e^{\int P d x} \frac{d y}{d x}+\)…
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