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The General Solution of a Differential Equation of the Type D X D Y + P 1 X = Q 1 is - CBSE (Commerce) Class 12 - Mathematics

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Question

The general solution of a differential equation of the type \[\frac{dx}{dy} + P_1 x = Q_1\] is

  • \[y e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]

  • \[y e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]

  • \[x e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]

  • \[x e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]

Solution

\[x e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]

 

We have,

\[\frac{dx}{dy} + P_1 x = Q_1\]

Comparing with the equation \[\frac{dx}{dy} + Px = Q\], we get

P = P1

Q = Q1

The general solution of the equation \[\frac{dx}{dy} + Px = Q\] is given by \[x e^{\int Pdy} = \int\left\{ Q e^{\int Pdy} \right\}dy + C\]       ...(1)

Putting the value of P and Q in (1), we get

\[x e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]

  Is there an error in this question or solution?
Solution The General Solution of a Differential Equation of the Type D X D Y + P 1 X = Q 1 is Concept: General and Particular Solutions of a Differential Equation.
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