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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

ConceptGeneral and Particular Solutions of a Differential Equation

#### 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?

#### Video TutorialsVIEW ALL [2]

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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