Question

If y = A/x be the solution of the value 6ydx + 6xdy = 0 under y(- 1) = 1 then value of A is
​

Answer 1

Answer:

Answer

3

xdy=ydx+y

2

dy

−y

2

dy=ydx+y

2

dy

dy=

−y

2

ydx−xdy

(usiny formula

−y

2

ydx−xdy

=d(

y

x

))

dy=−(d(

y

x

))

Integrating both side worot x

⇒y=

y

−x

+c

1

now,

y(I)=1Ifx=1,y=1

⇒I=

I

−1

+c

1

c

1

=2

y=

y

−x

+2

Ifx=−3

⇒y=

y

+3

+2

⇒y

2

−2y−3=0

⇒y

2

−3y+y−3=0

⇒y(y−3)+1(y−3)=0

⇒(y−3)(y+1)=0

y=3,−1

Hence,

y=3

Answer 2

Concept:

An ordinary or partial derivative of an unknown function is contained in a differential equation. The functions in most applications represent physical values, the derivatives their rates of change, and the differential equation the connection between the two. A differential equation is one in which the dependent variable's derivative with respect to the independent variable is involved.

Find:

The value of A.

Solution:

$6ydx+6xdy=0\\ydx+xdy=0$

Divide the equation by $xy$ on both sides.

$\frac{dx}{x}+\frac{dy}{y} =0$

Integrate on both sides.

$logx+logy=logc\\log(xy)=logc\\xy=c\\y=\frac{c}{x}$

$y=\frac{A}{x}$

Substitute the value $-1$ in x.

$1=\frac{A}{-1} \\A=-1$

Hence, the value of A is $-1$.

#SPJ3