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Solution for The General Solution of a Differential Equation of the Type D X D Y + P 1 X = Q 1 is (A) Y E ∫ P 1 D Y = ∫ { Q 1 E ∫ P 1 D Y } D Y + C (B) Y E ∫ P 1 D Y = ∫ { Q 1 E ∫ P 1 D Y } D Y + - CBSE (Science) 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
(a) \[y e^\int P_1 dy = \int\left\{ Q_1 e^\int P_1 dy \right\}dy + C\]
(b) \[y e^\int P_1 dy = \int\left\{ Q_1 e^\int P_1 dy \right\}dy + C\]
(c) \[x e^\int P_1 dy = \int\left\{ Q_1 e^\int P_1 dy \right\}dy + C\]
(d) \[x e^\int P_1 dy = \int\left\{ Q_1 e^\int P_1 dy \right\}dy + C\]

Solution

\[\left( c \right) x e^\int P_1 dy = \int\left\{ Q_1 e^\int P_1 dy \right\}dy + C\] 
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 
\[x e^\int Pdy = \int\left\{ Q e^\int Pdy \right\}dy + C\]
  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 (A) Y E ∫ P 1 D Y = ∫ { Q 1 E ∫ P 1 D Y } D Y + C (B) Y E ∫ P 1 D Y = ∫ { Q 1 E ∫ P 1 D Y } D Y + Concept: General and Particular Solutions of a Differential Equation.
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