The general solution of the differential equation dydx-3x-4y-14x-2y-3 iswhere c is constant of integration

Dydx=3x 4y+14x+2y+3 ⇒ (4x+2y+3)dy=(3x 4y+1)dx ⇒ 4(xdy+ydx)+2ydy+3dy 3xdx dx=0 ⇒ 4d(xy)+2ydy+3dy 3xdx dx=0 Integrating both sides, we get ⇒ 4xy+y^2+3y 3x^22 x=c ...

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Standard XII

Mathematics

Equations Reducible to Standard Forms

The general s...

Question

The general solution of the differential equation $\frac{d y}{d x} = \frac{3 x - 4 y + 1}{4 x + 2 y + 3}$ is
(where $c$ is constant of integration)

4 x y + y^{2} - \frac{3 x^{2}}{2} - 3 x = c

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4 x y + y - \frac{x^{2}}{2} - x = c

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4 x y + 3 y - \frac{3 x^{2}}{2} - x = c

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4 x y + y^{2} + 3 y - \frac{3 x^{2}}{2} - x = c

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Solution

The correct option is D $4 x y + y^{2} + 3 y - \frac{3 x^{2}}{2} - x = c$
$\frac{d y}{d x} = \frac{3 x - 4 y + 1}{4 x + 2 y + 3}$
$\Rightarrow (4 x + 2 y + 3) d y = (3 x - 4 y + 1) d x$
$\Rightarrow 4 (x d y + y d x) + 2 y d y + 3 d y - 3 x d x - d x = 0$
$\Rightarrow 4 d (x y) + 2 y d y + 3 d y - 3 x d x - d x = 0$
Integrating both sides, we get
$\Rightarrow 4 x y + y^{2} + 3 y - \frac{3 x^{2}}{2} - x = c$

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Equations Reducible to Standard Forms

Standard XII Mathematics

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The general solution of the differential equation dydx=3x−4y+14x+2y+3 is (where c is constant of integration)

The correct option is D 4xy+y2+3y−3x22−x=cdydx=3x−4y+14x+2y+3 ⇒(4x+2y+3)dy=(3x−4y+1)dx ⇒4(xdy+ydx)+2ydy+3dy−3xdx−dx=0 ⇒4d(xy)+2ydy+3dy−3xdx−dx=0 Integrating both sides, we get ⇒4xy+y2+3y−3x22−x=c

The general solution of the differential equation $\frac{d y}{d x} = \frac{3 x - 4 y + 1}{4 x + 2 y + 3}$ is
(where $c$ is constant of integration)