Calculus

Consider the differential equation dy/dx = x^2(y - 1). Find the particular solution to this differential equation with initial condition f(0) = 3.

I got y = e^(x^3/3) + 2.

  1. 👍 0
  2. 👎 0
  3. 👁 1,741
  1. assuming that your answer is correct
    dy/dx = x^2 e^(x^3/3)
    but
    e^(x^3/3) = y-2
    so
    dy/dx = x^2 (y-2) hummm

    I'll try
    dy/(y-1) = x^2 dx

    ln(y-1)= x^3/3 + c

    (y-1) = e^[x^3/3 + c]
    y-1 = e^(x^3/3) e^c
    y-1 = Ce^(x^3/3)
    y = 1 + Ce^(x^3/3)

    3 = 1 + C
    C = 2

    so
    y = 1 + 2e^(x^3/3)

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    Suppose that we use Euler's method to approximate the solution to the differential equation 𝑑𝑦/𝑑π‘₯=π‘₯^4/𝑦 𝑦(0.1)=1 Let 𝑓(π‘₯,𝑦)=π‘₯^4/𝑦. We let π‘₯0=0.1 and 𝑦0=1 and pick a step size β„Ž=0.2.

  2. CALC

    Find the particular solution of the given differential equation dydx=βˆ’4xe(yβˆ’x^2);y=11whenx=1. THanks

  3. Differential Equations

    The velocity v of a freefalling skydiver is well modeled by the differential equation m*dv/dt=mg-kv^2 where m is the mass of the skydiver, g is the gravitational constant, and k is the drag coefficient determined by the position

  4. AP Calculus Help Five Questions

    1. Find the particular solution to y " = 2sin(x) given the general solution y = -2sin(x) + Ax + B and the initial conditions y(pi/2) = 0 and y'(pi/2) = -2. 2. What function is a solution to the differential equation y ' - y = 0?

  1. Calculus

    Consider the differential equation dy/dx = x^4(y - 2). Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 0. Is this y=e^(x^5/5)+4?

  2. Help with differential eqs problem???? (Calculus)

    Consider the differential equation dy/dt=y-t a) Determine whether the following functions are solutions to the given differential equation. y(t) = t + 1 + 2e^t y(t) = t + 1 y(t) = t + 2 b) When you weigh bananas in a scale at the

  3. Calculus

    Consider the differential equation dy/dx = 2x - y. Let y = f(x) be the particular solution to the differential equation with the initial condition f(2) = 3. Does f have a relative min, relative max, or neither at x = 2? Since

  4. Differential equations in Calculus...plsssss help?

    Suppose that represents the temperature of a cup of coffee set out in a room, where T is expressed in degrees Fahrenheit and t in minutes. A physical principle known as Newton’s Law of Cooling tells us that dT/dt = -1/15T+5 15T

  1. Calculus

    For Questions 1–3, use the differential equation given by dx equals xy/3, y > 0. Complete the table of values x βˆ’1 βˆ’1 βˆ’1 0 0 0 1 1 1 y 1 2 3 1 2 3 1 2 3 dy/dx ? ? ? ? ? ? ? ? ? Find the particular solution y = f(x) to the

  2. Calculus!!

    Consider the differential equation given by dy/dx = xy/2. A. Let y=f(x) be the particular solution to the given differential equation with the initial condition. Based on the slope field, how does the value of f(0.2) compare to

  3. math

    Consider the differential equation dy/dx = -1 + (y^2/ x). Let y = g(x) be the particular solution to the differential equation dy/ dx = -1 + (y^2/ x) with initial condition g(4) = 2. Does g have a relative minimum, a relative

  4. I would like to understand my calc homework:/

    Consider the differential equation given by dy/dx=(xy)/(2) A) sketch a slope field (I already did this) B) let f be the function that satisfies the given fifferential equation for the tangent line to the curve y=f(x) through the

You can view more similar questions or ask a new question.