Solve the IVP. dy/dt - 2ty = -6t^2 e^(t^2) ; y(0) = 1

Question.

Solve the IVP.
dy/dt - 2ty = -6t^2 e^(t^2) ; y(0) = 1

Solution:

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 differential equation y' = 8x - y

Question.

Solve the differential equation
y' = 8x - y

Solution:

Solve the differential Equation dy/dt = yt^2 + 4

Question.

Solve the differential Equation

dy/dt = yt² + 4

Solution:

Solve the IVP y' + y = sin(t) + cos(t) with y(0) = 1 by A) method of undetermined coefficients and B) method of variation of parameters

Question.

Solve the IVP y' + y = sin(t) + cos(t) with y(0) = 1 by

A) method of undetermined coefficients and

B) method of variation of parameters


Solution:

Solve the IVP y' + y = te^(-t) with y(0) = 0 by A) method of undetermined coefficients and B) method of variation of parameters

Question.

Solve the IVP y' + y = te^(-t) with y(0) = 0 by

A) method of undetermined coefficients and

B) method of variation of parameters


Solution:

Solve the IVP y' + y = (e^t) cos(t) + (e^t) sin(t) with y(0)=1 by A) method of undetermined coefficients B) method of variation of parameters

Question.

Solve the IVP y' + y = (e^t) cos(t) + (e^t) sin(t) with y(0)=1 by

A) method of undetermined coefficients

B) method of variation of parameters

Solution:

Solve the IVP xy'-2y=x^2+6 , with y(1)=1 by method of variation of parameters

Question.

Solve the IVP xy' - 2y = x² + 6 , with y(1)=1 by method of variation of parameters

Solution:

Solve the IVP y' + (tan t)y = 2sec(t) tan(t), y(0)=0 by method of variation of parameters Plot the solution y=y(t) on 0<= t < (pi/2) and compute lim as t -> (pi/2^-) of y(t)

Question.

Solve the IVP y' + (tan t)y = 2sec(t) tan(t), y(0)=0 by method of variation of parameters

Plot the solution y=y(t) on 0<= t < (pi/2) and compute lim as t -> (pi/2^-) of y(t)

Solution:

Solve the given Linear DE subject to the indicated initial condition x dy/dx + y = x cos(x) ; y(pi) = 1

Question.


Solve the given Linear DE subject to the indicated initial

x dy/dx + y = x cos(x) ; y(pi) = 1


Solution:

Solve the Differential Equation dx/dy + 2xy = e^(-y^2)

Question.


Solve the Differential Equation

dx/dy + 2xy = e^(-y²)

Solution:

Given the initial value problem y' + 2xy = 4x , y(0)=3 a) classify the DE by type, order and linearity. b) Give an interval I where the solution is defined and is unique. c) Solve the above IVP

Question.

Given the initial value problem

y' + 2xy = 4x , y(0)=3

a) classify the DE by type, order and linearity.

b) Give an interval I where the solution is defined and is unique.

c) Solve the above IVP

Solution:

Find the general solution of each of the following equations. (a) x^2y' + 3xy =1 (b) (1+e^x)y' + 2e^xy = (1+e^x)e^x (c) y' = cos x - y tan x

Question. Find the general solution of each of the following equations.

(a) x²y' + 3xy =1
(b) (1+e^x)y' + 2e^xy = (1+ex)e^x
(c) y' = cos x - y tan x

Solution.

Solve analytically for the exact particular solution for the Initial Value Problem. y'+y=2e^x , y(0)=7

Question. Solve analytically for the exact particular solution for the Initial Value Problem.

y'+y=2e^x , y(0)=7

Solution:

dy/dx = (x - y)/x

dy/dx= sin(3x)/x^2 - 2y/x

dy/dx + y = x