Q. 225.0( 1 Vote )

# Solve the followi

Given: differential equation xdy – (y + 2x2) dx = 0

To find: the value of given differential equation

given: xdy – (y + 2x2) dx = 0

Dividing throughout by dx,

Dividing throughout by x we get,

This is of the of the standard form, i.e.,

Where and Q=2x

And we know the integrating factor is

IF=e∫P dx

Substituting the value of P in the IF, we get

But we know integration of is log x, substituting this in athe bove equation, we get

IF=e-log( x)

Or,

But elog x=x, so he above equation becomes,

IF=x-1

So the general solution of a differential equation is

y(IF)=∫(Q×I.F)dx+C

Substituting the corresponding values in the above equation, we get

On integrating, we get

Or

y=2x2+Cx

Hence this is the solution of the given differential equation

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