For each of the differential equations in question, find a particular solution satisfying the given condition:
(x³ + x² + x + 1) dy/dx = 2x² + x, y = 1 when x = 0

Question

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

Philoid · Accepted Answer

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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)

For each of the differential equations in question, find a particular solution satisfying the given condition:(x3 + x2 + x + 1) dy/dx = 2x2 + x, y = 1 when x = 0

For each of the differential equations in question, find a particular solution satisfying the given condition:
(x³ + x² + x + 1) dy/dx = 2x² + x, y = 1 when x = 0