# 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 f(0)? Justify your answer.

B. Find the particular solution y = f(x) to the given differential equation with the initial condition f(0) = 3. Use your solution to find f(0.2).

1. 👍
2. 👎
3. 👁
1. dy/dx = xy/2
dy/y = x/2 dx
ln y = 1/4 x^2 + c
y = c e^(x^2/4)

1. 👍
2. 👎
2. khv

1. 👍
2. 👎

## Similar Questions

1. ### Calc 2

Find the solution of the differential equation that satisfies the given initial condition. dy/dx= x/y, y(0) = −7

2. ### Calculus

Suppose that we use Euler's method to approximate the solution to the differential equation 𝑑𝑦/𝑑𝑥=𝑥^4/𝑦 𝑦(0.1)=1 Let 𝑓(𝑥,𝑦)=𝑥^4/𝑦. We let 𝑥0=0.1 and 𝑦0=1 and pick a step size ℎ=0.2.

3. ### Differential Equation

What is the solution of the differential equation of (6x+1)y^2 dy/dx + 3x^2 +2y^3=0?

4. ### Differential Equations

Consider the differential equation: dy/dt=y/t^2 a) Show that the constant function y1(t)=0 is a solution. b)Show that there are infinitely many other functions that satisfy the differential equation, that agree with this solution

1. ### Calc

Consider the differential equation dy/dx=-2x/y Find the particular solution y =f(x) to the given differential equation with the initial condition f(1) = -1

2. ### 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

3. ### 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?

4. ### 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

1. ### Calculus BC

Let y = f(x) be the solution to the differential equation dy/dx=y-x The point (5,1) is on the graph of the solution to this differential equation. What is the approximation of f(6) if Euler’s Method is used given ∆x = 0.5?

2. ### Calculus

Verify that the function y(x)= x - (1/x) is a solution to the differential equation, xy'+ y= 2x I have absolutely no clue what to do with that + y Please help :c

3. ### Calculus

Using separation of variables, solve the following differential equation with initial conditions dy/dx = e^(2x+3y) and y(0) = 1. Hint: use a property of exponentials to rewrite the differential equation so it can be separated

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