For the below ordinary differential equation, state the order and determine if the equation is linear or nonlinear. Then find the general solution of the ordinary differential equation. Verify your solution. dy/dx = 2y

Question.

For the below ordinary differential equation, state the order and determine if the equation is linear or nonlinear. Then find the general solution of the ordinary differential equation. Verify your solution.

dy/dx = 2y


Solution:

Solve the separable differential equation dy/dx = -0.8/cos(y) with initial condition y(0) = pi/4

Question.

Solve the separable differential equation dy/dx = -0.8/cos(y) with initial condition y(0) = pi/4

Solution:

Solve the separable differential equation y’ = sqrt(-2y + 41) with initial condition y(-5) = 8

Question.

Solve the separable differential equation y’ = sqrt(-2y + 41) with initial condition y(-5) = 8

Solution:

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

Question.

dy/dx=(1+y^2)/(y+yx²)


Solution:

Find the explicit solution of the differential equation that satisfies the given initial condition. y dy/dx = xe^(-y^2) , y(0) = -3

Question.

Find the explicit solution of the differential equation that satisfies the given initial condition.

y dy/dx = xe^(-y^2) , y(0) = -3

Solution:

Find the solution to the following separable differential equation y' = ye^x

Question.

Find the solution to the following separable differential equation.

y’ = ye^x

Solution:

Solve the separable Differential Equation dy/dx = e^(3x+4y)

Question. Solve the separable Differential Equation dy/dx = e^(3x+4y)


Solution:

dy/dx = 3e^(2x) , y(0) = 5/2

dy/dx = 3x^2 y^2 - y^2

Find the general solution to the differential equation
dy/dx = 3x^2 y^2 - y^2
Find the particular solution for which y(0) = 1 ie when x = 0 , y =1

dy/dx = 1/(x^2 - 3x) , y(4) = (2/3) ln(4)

Solve the initial value problem and give the interval of definition.
dy/dx = 1/(x^2 - 3x) , y(4) = (2/3) ln(4)

dy/dx= xy + 7x +2y + 14

dy/dx= xy + 7x +2y + 14