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Differential Calculus

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19 Apr 2009 21:42:06 IST

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393

differential eqns....

None

for differential eqn.......

general solution is .

then,

rates no doubt.......

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Rajat Sen

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Joined: 7 Aug 2007

Posts: 533

20 Apr 2009 06:58:43 IST

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let $y=vx$
$\frac{dy}{dx}=v+x\frac{dv}{dx}$
let $f(v)=\phi\left(\frac{1}{v}\right)$
Putting back in the equation we get :
$x\frac{dv}{dx}=f(v)$
so,
$\int \frac{dv}{f(v)}=\int \frac{dx}{x}$
Now if $\int \frac{dv}{f(v)} = \frac{1}{v}$ then we get the required solution!
so,
$\phi\left(\frac{1}{v}\right)=f(v)=-v^{2}$
so,
$\phi\left(\frac{x}{y}\right)=-\frac{y^{2}}{x^{2}}$
Idea !

saharsha kumar keshkar

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Joined: 7 Aug 2008

Posts: 1104

20 Apr 2009 08:41:37 IST

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