Calculus

posted by .

Solve the differential and initial value problem:

x(dy/dx) + 1 = y^2

y(1)=0

I tried using bernoulli and it didn't quite work.

  • Calculus -

    xy' + 1 = y^2
    xy' = y^2-1
    y' = (y^2-1)/x
    dy/(y^2-1) = dx/x
    arctanh(y) = log(x)
    or,
    log (1-y)/(1+y) = 2log(x)+c

    and you can massage that into exponentials and wind up with

    y = 1-e^(2cx^2) / 1+e^(2cx^2)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    how do you solve the initial value problem by using separation of variables dy/dx=1/y^2, y(0)=4
  2. calculus

    how do you solve the initial value problem by using separation of variables dy/dx=-xy^2 when y(1)=-0.25
  3. CALCULUS

    Using separation of variables technique, solve the following differential equation with initial condition dy/dx = (yx + 5x) / (x^2 + 1) and y(3) = 5. The solution is: a.) y^2 = ln(x^2 + 1) + 25 - ln10 b.) ln(abs(y+5)) = ln(x^2 + 1) …
  4. Differential Equation

    Solve the following initial-value problem: y"+6y'+5y=0; y(0)=0. y'(0)=3
  5. Differential Equations

    x dy/dx + y = 1/y^2, solve using bernoulli's equation. i got to du/dx + (2u)/x = 2x(u)^(-1/2). the u^(-1/2) is obviously a problem if im going to solve it using an integrating factor. if that is not what you yourself have gotten to …
  6. Calculus-HELP!!!!

    Show that the function y=c_1 e^x cos(x)+ c_2 e^x sin(x) satisfies the differential equation y''-2y'+2y=0 for any values of c1 and c2, then find the values for those constants that solve the initial value problem y(0)= 1, y'(0)= -1
  7. 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 to …
  8. Math/Calculus

    Solve the differential equation y'=3t^2+4. Solve the initial value problem y(0)=3. Separation of variables! My work: dy/dt= 3t^2+4 dy= 3t^2+4 dt Then you integrate both sides. ∫ dy= ∫ 3t^2+4dt Question: is there a 1 in …
  9. calculus

    1.Solve the differential equation dy/dx= y^2/x^3 for y=f(x) with the condition y(1) = 1. 2.Solve the differential equation y prime equals the product of 2 times x and the square root of the quantity 1 minus y squared. Explain why the …
  10. Help! Calculus

    I am so confused on how to solve this problem. I have it set up with y's on one side and x's on the other but I don't know what to do from there. Question: Solve the differential equation. The initial condition is y(0) = 1. ((x^2+1)^(1/2))(dy/dx) …

More Similar Questions