For the following find: (Show detailed working) 1) general solution of the associated homogns DE 2) form...

For the following find: (Show detailed working)

1) general solution of the associated homogns DE

2) form of the particular solution associated with the undetermined coefficients method. Do not evaluate coefficients

a) (d² y / dx²) - dy/dx = x - 3

b) (d² y / dx²) + 2 dy/dx + y = (1+x)e^-x + x²

^c) (d² y / dx²) + y = sin(2x)

Expert Solution

milcah answered 2 years ago

a.) Show that the DE is exact and find a general solution 2y - y^2sec^2(xy^2)+[2x-2xysec^2(xy^2)]y' =...

a.) Show that the DE is exact and find a general solution 2y - y^2sec^2(xy^2)+[2x-2xysec^2(xy^2)]y' = 0 b.) Verify that the equation is not exact. Multiply by integrating factor u(x, y) = x and show that resulting equation is exact, then find a general solution. (3xy+y^2) + (x^2 + xy)dy/dx = 0 c.) Verify that the equation is not exact. Multiply by integrating factor u(x, y) = xy and show that resulting equation is exact, then find a general solution....

1. Find the general solution to the following ODE: y′′′+ 4y′= sec(2x) 2. Find the solution...

1. Find the general solution to the following ODE: y′′′+ 4y′= sec(2x) 2. Find the solution to the following IVP: 2y′′+ 2y′−2y= 6x2−4x−1 y(0) = −32 y′(0) = 5 3. Verify that y1=x1/2ln(x) is a solution to 4x2y′′+y= 0, and use reduction of order to find a second solution y2. 4. Find the general solutions to the following ODEs: a) y′′′−y′= 0. b) y′′+ 2y′+y= 0. c) y′′−4y′+ 13y= 0.

FIND THE GENERAL SOLUTION TO THE DE: Y”’ + 4Y” – Y’ – 4Y = 0...

FIND THE GENERAL SOLUTION TO THE DE: Y”’ + 4Y” – Y’ – 4Y = 0 COMPUTE: L {7 e 3t – 5 cos ( 2t ) – 4 t 2 } COMPUTE: L – 1 {(3s + 6 ) / [ s ( s 2 + s – 6 ) ] } SOLVE THE INITIAL VALUE PROBLEM USING LAPLACE TRANSFORMS: Y” + 6Y’ + 5Y = 12 e t WHEN : f ( 0 ) = -...

find the general solution of the equation using cauchy euler. show complete solution x^2 y" -...

find the general solution of the equation using cauchy euler. show complete solution x^2 y" - 3xy' + 3y = 2x^4 e^x

1) find the solution t the non-homogenous DE y''-16y=3e5x , y(0)=1 , y'(0)=2 2)find the solution...

1) find the solution t the non-homogenous DE y''-16y=3e5x , y(0)=1 , y'(0)=2 2)find the solution to the DE using cauchy-euler method x2y''+7xy'+9y=0 , y(1)=2 , y'(1)=3 3)find the solution to the DE using Laplace y''+8y'+16y=0 , y(0)=-1 , y'(0)=8

Obtain the general and particular solution of the DE d2 y(x) / d x2 + (1/2)...

Obtain the general and particular solution of the DE d2 y(x) / d x2 + (1/2) (dy(x) / dx) - (1/2)y(x) = x + 1 By use of the variation of parameters method. Evaluate all coefficients please.

Find the general solution to the DE: y'''+8y''+16y=0 (Hint: Find the auxilary equation first)

find the general solution of the following as follows Xn+2 = -2Xn+1 + 3Xn, x0=1 x1=2...

find the general solution of the following as follows Xn+2 = -2Xn+1 + 3Xn, x0=1 x1=2 a) find the 2x2 matrix that satisfies Yn+1=AYn b) Find the characteristic value of A and its corresponding characteristic vector c) express X0 = (1 2)as a linear combination of characteristic vector d) find Yn e) find Xn

PLEASE SHOW WORKING: find #1 cost sheet, job #2 cost sheet, general journal, t account (ledger)...

PLEASE SHOW WORKING: find #1 cost sheet, job #2 cost sheet, general journal, t account (ledger) and schedule of COGM, COGS and income. no project base given and asked in the comment 1 Step 1 You work for Thunderduck Custom Tables Inc. This is the first month of operations. The company designs and manufactures specialty tables. Each table is specially customized for the customer. This month, you have been asked to develop and manufacture two new tables for customers. You...

Find the general solution of this ODE: d^2y/dt^2+7 dy/dt+10y=5t^2−3t+6 The solution will be of the form:...

Find the general solution of this ODE: d^2y/dt^2+7 dy/dt+10y=5t^2−3t+6 The solution will be of the form: y(t)=Cy1(t)+Dy2(t)+yp(t) so use C and D as the arbitrary constants. y(t)=y(t)=

Question