The general solution of a differential equation of the type dx - dy - P 1 x - Q 1 isa ye - P 1 dy - Q 1 e - P 1 dy dy - Cb ye - P 1 dx - Q 1 e - P 1 dx dx - Cc xe - P 1 dy - Q 1 e - P 1 dy dy - Cd xe - P 1 dx - Q 1 e - P 1 dx dx - C

The integrating factor of the given differential equation dx/dy+P_1x=Q_1 is e^∫ P_1 dy The general solution of the differential equation is given by x. IF= ∫ (Q ...

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Byju's Answer

Standard XII

Mathematics

Linear Differential Equations of First Order

The general s...

Question

The general solution of a differential equation of the type $\frac{d x}{d y} + P_{1} x = Q_{1}$ is

(a) $y e^{\int P_{1} d y} = \int (Q_{1} e^{\int P_{1} d y}) d y + C$

(b) $y e^{\int P_{1} d x} = \int (Q_{1} e^{\int P_{1} d x}) d x + C$

(c) $x e^{\int P_{1} d y} = \int (Q_{1} e^{\int P_{1} d y}) d y + C$

(d) $x e^{\int P_{1} d x} = \int (Q_{1} e^{\int P_{1} d x}) d x + C$

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Solution

The integrating factor of the given differential equation $\frac{d x}{d y} + P_{1} x = Q_{1}$ is $e^{\int P_{1} d y}$

The general solution of the differential equation is given by

$x . I F = \int (Q \times I F) d y + C ∴ x e^{\int P_{1} d y} = \int (Q_{1} e^{\int P_{1} d y}) d y + C$

Hence, the correct option is (c).

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Similar questions

Q. The general solution of a differential equation of the type

\frac{d x}{d y} + P_{1} x = Q_{1}

is
(a)

y e^{\int P_{1} d y} = \int \{Q_{1} e^{\int P_{1} d y}\} d y + C

(b)

y e^{\int P_{1} d x} = \int \{Q_{1} e^{\int P_{1} d x}\} d x + C

(c)

x e^{\int P_{1} d y} = \int \{Q_{1} e^{\int P_{1} d y}\} d y + C

(d)

x e^{\int P_{1} d x} = \int \{Q_{1} e^{\int P_{1} d x}\} d x + C

Q. The general solution of a differential equation of the type

\frac{d x}{d y} + P_{1} x = Q_{1}

The general solution of differential equation $\frac{d y}{d x} = l o g x$ is

Q. Solution of the differential equation

y e^{x / y} d x = (x e^{x / y} + y^{2} sin y) d y

, is

Q. The solution of the differential equation.

y e^{x / y} d x = (x e^{x / y} + y^{2} sin y) d y

is.

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The general solution of a differential equation of the type dxdy+P1x=Q1 is (a) ye∫P1 dy=∫(Q1e∫P1 dy)dy+C (b) ye∫P1 dx=∫(Q1e∫P1 dx)dx+C (c) xe∫P1 dy=∫(Q1e∫P1 dy)dy+C (d) xe∫P1 dx=∫(Q1e∫P1 dx)dx+C

The integrating factor of the given differential equation dxdy+P1x=Q1 is e∫P1dy The general solution of the differential equation is given by x.IF=∫(Q×IF)dy+C ∴xe∫P1dy=∫(Q1e∫P1dy)dy+C Hence, the correct option is (c).