1. (a) Sketch the slope field for the given differential equation: dy/dx = 2? (b) Find...

1. (a) Sketch the slope field for the given differential equation: dy/dx = 2?

(b) Find the particular solution of the differential equation that satisfies the initial condition y(0) = 4

(c) What is the value of y when x = 1/2

2. (a) Find the general solution of the given differential equation: dy/dx = ysinx = ????? 2

(b) Find the particular solution of the differential equation that satisfies the initial condition ? = 2; ?ℎ?? ? = π/2

Expert Solution

Solution-

(a)

Draw the slope field using

the equation of slope,

only works with y and slope will increase with distance from x-axis (y values).

(b)

Particular solution,

satisfies (0,4)

(c)

Find value at x= 0.5

milcah answered 1 year ago

Find the general solution of the differential equation (x + 2y) (dx-dy) = dx + dy.

Consider the differential equation dy/dx = y^2 + y - 2 (1) Sketch its phase portrait...

Consider the differential equation dy/dx = y^2 + y - 2 (1) Sketch its phase portrait and classify the critical points. (2) Find the explicit solution of the DE.

Find dy/dx and d^2y/dx^2, and find the slope and concavity (if possible) at the given value...

Find dy/dx and d^2y/dx^2, and find the slope and concavity (if possible) at the given value of the parameter. (If an answer does not exist, enter DNE.) Parametric Equations Point x = et, y = e−t t = 3 dy/dx = d^2y/dx^2 = slope = concavity= ---Select--- concave upward concave downward neither

Sketch the direction field of the equation dy/dx=y-4y^3. Sketch the phase portrait. Find the equilibrium solutions...

Sketch the direction field of the equation dy/dx=y-4y^3. Sketch the phase portrait. Find the equilibrium solutions and classify each equilibrium as stable, unstable or semi-stable. Sketch typical solutions of the equation.

find the differential equation of dy/dx = y+y^3

Consider the curve given by the equation y^2 - 2x^2y = 3 a) Find dy/dx. b)...

Consider the curve given by the equation y^2 - 2x^2y = 3 a) Find dy/dx. b) Write an equation for the line tangent to the curve at the point (1, -1). c) Find the coordinates of all points on the curve at which the line tangent to the curve at that point is horizontal. d) Evaluate d 2y /dx2 at the point (1, -1).

Question

1. (a) Sketch the slope field for the given differential equation: dy/dx = 2? (b) Find...

Solutions

Expert Solution

Related Solutions

Find the general solution of the differential equation (x + 2y) (dx-dy) = dx + dy.

Consider the differential equation dy/dx = y^2 + y - 2 (1) Sketch its phase portrait...

Find dy/dx and d^2y/dx^2, and find the slope and concavity (if possible) at the given value...

Sketch the direction field of the equation dy/dx=y-4y^3. Sketch the phase portrait. Find the equilibrium solutions...

find the differential equation of dy/dx = y+y^3

Consider the curve given by the equation y^2 - 2x^2y = 3 a) Find dy/dx. b)...

Find The solution of the Differential Equation of (y+4x+2)dx - dy = 0, y(0) = 3...

Given the differential equation dy/dx =x. With intitial condition y(1)=0.5. Use eulers method with dx =...

differential equation y'=dy/dx = -(3xey+2y)/ (x2ey+x). find the solution

Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. dy dx...