If y x is the solution of the differential equation x -2 dy - dx - x 2-4 x -9- x -2 and y 0-0- then y -4 is equal toA- 0B- 2C- -1D- 1

The correct option is A 0 We can write differential equation as dy/dx=x^2+4x 9/x+2=x+2 13/x+2 ⇒ y=1/2(x+2)^2 13 log |x+2|+C As y(0)=0 we get 0=2 13 log |2|+C o ...

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Standard XII

Mathematics

Integrating Factor

If y x is the...

Question

If $y (x)$ is the solution of the differential equation $(x + 2) \frac{d y}{d x} = x^{2} + 4 x - 9, x \neq 2$ and $y (0) = 0$ , then $y (- 4)$ is equal to

$2$

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$- 1$

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$0$

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Solution

The correct option is D
$0$

We can write differential equation as

$\frac{d y}{d x} = \frac{x^{2} + 4 x - 9}{x + 2} = x + 2 - \frac{13}{x + 2}$

$\Rightarrow y = \frac{1}{2} (x + 2)^{2} - 13 log | x + 2 | + C$

As $y (0) = 0$ we get

$0 = 2 - 13 log | 2 | + C$ or $C = 13 log 2 - 2$

Also, $y (- 4) = 2 - 13 log 2 + 13 log 2 - 2 = 0$

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If y(x) is the solution of the differential equation (x+2)dydx=x2+4x−9, x≠2 and y(0)=0, then y(−4) is equal to

The correct option is D 0 We can write differential equation as dydx=x2+4x−9x+2=x+2−13x+2 ⇒y=12(x+2)2−13 log |x+2|+C As y(0)=0 we get 0=2−13 log |2|+C or C=13 log 2−2 Also, y(−4)=2−13 log 2+13 log 2−2=0

If $y (x)$ is the solution of the differential equation $(x + 2) \frac{d y}{d x} = x^{2} + 4 x - 9, x \neq 2$ and $y (0) = 0$ , then $y (- 4)$ is equal to