Calculus - Seperable Equations

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!

  1. 👍 0
  2. 👎 0
  3. 👁 133
asked by COFFEE

Respond to this Question

First Name

Your Response

Similar Questions

  1. PLEEEEEAAAASE HELP WITH DIFFERENTIAL EQ PROBLEMS!!

    1) What are the equilibrium solutions to the differential equation and determine if it is stable or unstable with the initial condition y(-4)=1: 0.1(y+2)(4-y) 2) Use Euler's method with step size=0.5 and initial condition y(0)=3

    asked by Karen on December 8, 2014
  2. Calculus

    Solve the separable differential equation: dy/dt=4y^6 and find the particular solution satisfying the initial condition y(0)=-3 y(t)=?

    asked by Carly on July 29, 2011
  3. Calculus

    Solve the separable differential equation 10x−6ysqrt(x^2+1)dy/dx=0. with the initial condition y(0)=4.

    asked by Robin on November 18, 2013
  4. Calculus

    Which of the following is a separable, first-order differential equation? A) dy/dx= x+y/2x B) dy/dx=x+y/x-y C) dy/dx=sinx

    asked by Samantha on May 8, 2014
  5. Calculus

    Can you check my answer? Solve the separable differential equation: dy/dx=(sqrt(x))/2y y=(2/3)x^(3/4) Let f be the function given by f(x)=x^3-5x^2+3x+k is a constant. a) On what intervals is f is increasing? (-oo,1/3), (3,oo) b)

    asked by Anonymous on November 18, 2007
  6. calculus

    determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false a) the function f(x)=3/2 +cx^-2 is a solution of the differential equation xy'+2y=3

    asked by jhony on April 10, 2012
  7. Calculus

    Solve the differential equation dy/dx = -xe^y and determine the equation of the curve through P(1,2) I tried solving the differential equation and I get y = log(x^2/2 + C). Is this correct? Now I forgot how to find the equation.

    asked by Robert on August 6, 2012
  8. Differential equation (urgent pls!!!)

    Reduce the differential equation below to an exact equation (X - 2siny + 3)dx -(4siny - 2x + 3)dy=0. The problem here is how to solve for the integrating factor...any help pls?

    asked by BEN on March 4, 2016
  9. Physics

    For the harmonic potential V(x,y) = x^2 + y^2 a)Find the total differential, dV. b) Show that dV is exact c) Given that -dV = Fx.dx + Fy.dy where Fx and Fy is the force in the x and y direction, respectively, write a differential

    asked by Beth on November 14, 2008
  10. O.D.E

    If someone can help me with this ODE I would greatly appreciate it. Thank you in advance! ------ Consider the differential equation dx/dt = 1/2x This is a separable O.D.E., so we know how to find all of its solutions: they are of

    asked by Steve on April 25, 2016

More Similar Questions