Posted by **COFFEE** on Tuesday, June 26, 2007 at 12:17pm.

Solve the separable differential equation (dy/dx)=y(1+x) for y and find the exact value for y(.3).

dy/dx = y(1+x)

dy/y = (1+x)dx

Integral (dy/y) = Integral (1+x)dx

ln (y) = x + (1/2)x^2 + C

y = e^(x + (1/2)x^2 + C)

y(0.3) = e^(0.345 + C)

I am stuck here. How do I solve for C to get the exact value?

Thanks!

y = e^(x + (1/2)x^2 + C)

(0.3) = e^.3 * e^.045 * e^C

e^c= .3/(e^.345)

c= ln ( .3/(e^.345) )

y = e^(x + (1/2)x^2 + C)

(0.3) = e^.3 * e^.045 * e^C

e^c= .3/(e^.345)

c= ln ( .3/(e^.345) )

So I plug in 0.3 for both x and y?

The exact value of y(0.3) would be:

y(0.3)=e^((0.3)+(1/2)(0.3)^2+(ln(0.3/0.345)))

Is this correct? Thanks.

OOps, I copied your work without thinking.

y = e^(x + (1/2)x^2 + C)

now, to solve for c, you have to have some boundry value, ie, the y for a given x. Then you solve for c.

Sorry, I wasn't thinking.

That's ok...I forgot to post the condition of dy/dx=y(1+x), y(0)=1...sorry!

So it would be:

y = e^(x + (1/2)x^2 + C)

1 = e^(0 + (1/2)0^2 + C)

1 = e^C

ln(1) = C

C = 0

Then...y = e^(x + (1/2)x^2)

y(0.3) = e^(0.3 + (1/2)(0.3^2))

y(0.3) = e^0.345

And that's it, correct?

Yes.

Thank You!

help me solve this problem..

solve for W: 2L+2W=38

please and thank you!

## Answer this Question

## Related Questions

- differential equations - the directions are to determine whether or not the ...
- Calculus II/III - A. Find the integral of the following function. Integral of (x...
- calculus - LEt f and g be continous functions with the following properties i. ...
- calculus - LEt f and g be continous functions with the following properties i. ...
- Math - I need to solve this set of differential equations {y'+(t/2)1, y(0)=1} ...
- Differential Equations - Solve the seperable differential equation for U. du/dt...
- Calculus - Center of Mass - Find the exact coordinates of the centroid given the...
- PLEEEEEAAAASE HELP WITH DIFFERENTIAL EQ PROBLEMS!! - 1) What are the equilibrium...
- Math/Calculus - How would I solve the following integral with the substitution ...
- calculus - use the trapezoidal and simpson's rule to approximate the value of ...