doubt

xdy=y(dx+ydy) if y(1)=1 nd y(x)>0 then find y(-2)

9 Answers

1357
Manish Shankar ·

it is xdy-ydx=y2dy

(xdy-ydx)/y2=dy

d(-x/y)=dy

now you can complete it

1
smsm ·

i have done upto this ,solve after this. i am not getting the ans

1357
Manish Shankar ·

Put x = y2t

=> dy/dx = -y/2t dt/dx

can you explain this

4
UTTARA ·

x = y2t

Differentiating wrt x on both sides

1 = 2y dy/dx t + y2dt/dx

=>1 - dy/dx 2yt = y2 dt/dx

=>dy/dx = [ 1-y2dt/dx ]/2yt

So , 1 - y2dt/dx = 2y2t/y2(1-t)

=> integ [ 1-t/t(1-3t) ] dt = integ [ 1/x] dx

=>2 ln (1-3t) + ln t = ln x + c

=> ln (1-3t)2t = lnx + c

1
smsm ·

manish , express that as funtion of y

62
Lokesh Verma ·

Uttara.. i think there is a slight calculation mistake.. try to see that nicely :)

4
UTTARA ·

@Nishant Sir i editted the solution!!! : )

62
Lokesh Verma ·

I still think there is a mistake in

So , 1 - y2dt/dx = 2y2t/y2(1-t) step... I could not understand taht!

1
$ourav @@@ -- WILL Never give ·

yes,i also couldnt understand dat.......

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