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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

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

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

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

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

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

#### 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?

#### 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 Concept: General and Particular Solutions of a Differential Equation.
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