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The integrating factor of differential equation $R\frac{dx}{dy} + Px = Q$ where P, Q, R are functions of y is
APPLY KNOWLEDGE 1 Marks
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Calculation / Logic
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Q: The integrating factor of differential equation $R\frac{dx}{dy} + Px = Q$ where P, Q, R are functions of y is

Question Analysis & Solution

Detailed Solution

Step 1: Standardize the Differential Equation

The given differential equation is R(dx/dy) + Px = Q. To find the integrating factor, we must first convert this into the standard linear form: dx/dy + P'(x) = Q'. Dividing the entire equation by R, we get: $$ \frac{dx}{dy} + \frac{P}{R}x = \frac{Q}{R} $$

Step 2: Identify the Coefficient of x

Comparing the standardized equation with the general form dx/dy + P_1(y)x = Q_1(y), we identify the coefficient of x as: $$ P_1(y) = \frac{P}{R} $$

Step 3: Calculate the Integrating Factor (IF)

The formula for the integrating factor of a linear differential equation in x is given by: $$ IF = e^{\int P_1(y) dy} $$ Substituting the value of P_1(y): $$ IF = e^{\int \frac{P}{R} dy} $$

Final Answer: Option (C)

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