Q. 113.5( 71 Votes )

# For each of the differential equations in question, find a particular solution satisfying the given condition:

(x^{3} + x^{2} + x + 1) dy/dx = 2x^{2} + x, y = 1 when x = 0

Answer :

(

Separating variables,

Integrating both sides,

Integrating it partially,

Now comparing the coefficients of

⇒ A + B = 2

⇒ B + C = 1

⇒ A + C = 0

Solving them we will get the values of A,B,C

Putting the values of A,B,C in i)

So,

Then, 2xdx = dt

or,

Or,

Now, we are given that y = 1 when x = 0

So,

C = 1

Putting the value of c in ii)

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