P4 - 2 differential eqn toufies

anyone pls. help me solve this

dy/dx - (1+3x^-1)y = x + 2, y(1) = e -1

The answer to this is y = -x + x3ex.

and the next qn. is

dy/dx + y + x/y = 0

would be grateful for all ur help

Reply 1

Christophicus

studentruzaika

anyone pls. help me solve this

dy/dx - (1+3x^-1)y = x + 2, y(1) = e -1

The answer to this is y = -x + x3ex.

and the next qn. is

dy/dx + y + x/y = 0

would be grateful for all ur help

I'm willing to help, but I can't understand the initial conditions for the first one.
y(1) = e -1 :confused:

Reply 2

Fade Into Black

Is there anything els you can write in terms of a fuller question? Its a bit vague you've given us the answer but im not sure entirely wat you want 2 be found and is y=e-1 a subsititution?

Reply 3

studentruzaika

Fade Into Black

Is there anything els you can write in terms of a fuller question? Its a bit vague you've given us the answer but im not sure entirely wat you want 2 be found and is y=e-1 a subsititution?

its the value of y at 1 hence y(1)

Reply 4

Christophicus

I'm sorry but the question is very badly typed.
Is it e^-1 or e - 1?

Reply 5

7589200

I get the integrating factor to be 1/(e^x x^3) - which sets up a couple of horrible integrals.

Reply 6

Christophicus

studentruzaika

anyone pls. help me solve this

dy/dx - (1+3x^-1)y = x + 2, y(1) = e -1

The answer to this is y = -x + x3ex.

INTEGRATING FACTOR is 1/(x^3.e^x)

x^-3.e^-x.dy/dx + (-x^-3.e^-x -3x^-4.e^-x)y = (x+2)/(x^3.e^x)
=> d(x^-3.e^-x.y)/dx = (x+2)/(x^3.e^x)
=> x^-3.e^-x.y = (x+2)/(x^3.e^x) = x^-2.e^-x + 2x^-3.e^-x

That's as far as I get. Now if someone could intepret what the OP has typed that would be very useful.