# If  y(x) is the solution of the differential equation Option 1) 0 Option 2) 1 Option 3) -1 Option 4) 2

V Vakul

As we learnt in

Solution of Differential Equation -

$\frac{\mathrm{d}y }{\mathrm{d} x} =f\left ( ax+by+c \right )$

put

$Z =ax+by+c$

- wherein

Equation with convert to

$\int \frac{dz}{bf\left ( z \right )+a} =x+c$

$(x+2)\frac{dy}{dx}=x^{2}+4x-9$

$\int dy=\int \frac{x^{2}+4x-9}{x+2}dx$

$\int dy=\int \frac{x^{2}+4x+4-13}{x+2}dx$

$=\int \frac{(x+2)^{2}}{(x+2)}dx -\int \frac{13}{x+2}dx$

$=\int (x+2)dx-\int \frac{13}{x+2}dx$

$y=\frac{x^{2}}{2}+2x-13\ log\left | x+2 \right |+C$

$0=0+0-13\ log2+C$

$\therefore C=13\ log2$

$y=\frac{x^{2}}{2}+2x-13log\left | x+2 \right |+13\ log2$

$y=\frac{16}{2}-8-13\ log\left | -4+2 \right |+13\ log2$

=8 - 8 - 1 log | 2 | + 13 log 2 = 0

Option 1)

0

This option is correct

Option 2)

1

This option is incorrect

Option 3)

-1

This option is incorrect

Option 4)

2

This option is incorrect

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