d*y Obtain a particular solution for dx+ d²y + + dx² * + y = x³ + 2x + 1 dx

Q: Determine the quadrants in which the solution of the differential equation dy/dx = (1/2)xy is an…

A:

Q: dy 2y_(x+2)² %3D dx x2 -4 x² -4

A:

Q: day dx2 -2 dy x +y = dx +y = 2 cos x

A: We have to find the solution to the given differential equation d2ydx2-2dydx+y=2 cosx, y0=0 and y7=7

Q: Find afunction yp that is a solutionto the differential equation,y′′+y′=2e2x+cos(x).

A: To find the solution y"+y'=2e2x+cosx

Q: Don’t skip any steps. Solve the separable differential equation : dy/dx = 3x^2y, y(0) = 2

A:

Q: 2. (D? — 2D + 5) у — 252? + 12

A:

Q: Show that the solution, of the differential 5x3 is of у — ху? — х*у dy equation: dx xy² – x²y – 2r³…

A:

Q: Solve the differential equation 5(duldx)+3(du/dy)=2u using the method of separation of variables if…

A:

Q: Find the values of the constant r so that y = e™* satisfies the differential equation 2y" + y' — у…

A:

Q: Solve for the particular solution of the following differential equUations. a. (x³ + 3y)dx –- xdy;…

A: The given differential equation is: x3+3ydx-x dy=0 ;    y(1)=3

Q: Find the general solution of dx dy xy+3x-y-3 xy-2x+4y-8

A: Given differential equation is  dxdy=xy+3x-y-3xy-2x+4y-8

Q: 9. Find the particular integral of differential equation (D² +a² ]y =bcosax.

A: Particular integral of the second order differential equation.

Q: The integral factor for the Linear Differential equation 4 - !y= x0 is -I Select one: O True O False

A: For the first order Linear differential equations:

Q: Verify that y(x)=exsinx is a solution to the differential equation   2ycotx-d2y/dx2=0

A: Consider the given solution to the D.E. Differentiate it w.r.t x twice to get the double derivative…

Q: Make an appropriate substitution to find a solution of the equation dy/dx = sin(x – y). Does this…

A:

Q: 2ydx + x(2 + x²y) dy = 0

A:

Q: 7. (xy² – 2y)dx + (3 – 2xy²)dy = 0

A:

Q: 3. (D³ – 3D² +4)y = 40cos2x + 6

A: Given, D3-3D2+4y=40 cos2x+6 Its auxiliary equation is, m3-3m2+4=0⇒m+1m-22⇒m=-1,2,2 Hence,…

Q: 5. x'dy-y'dx= xydy

A:

Q: 4. Solve the homogeneous differential equation x’dy+(y² +xydx=0.

A:

Q: SHOW YOUR SOLUTION: Solve the constant of integration of the given differential equation xdi+6ydy=0…

A:

Q: The differential equation dy/dx = y(y+6) has initial condition of y(0) = 3 What is y(1)? Multiple…

A: Given

Q: (x²+y)dx + dy 0

A: This linear differential equation

Q: Solve the Nou-linear differential equation casy Sinylla@şiny given that 4(0)=6

A:

Q: Find the solution to the differential equation dy/dx + y^2sin(x) = 0 which satisfies y(0) = −1.

A:

Q: The differential equation (xy2 + y)dy = (x + 1)dx is separable. Select one: O True OFalse

A: We have to find

Q: 6T y" – 12y' + (36 + sin - -60e7x

A: The given function is,y''-12y'+36+sin6π2y=-60e7x

Q: THE

A: Please refer to the image below

Q: FIND THE GIVEN DIFFERENTIAL EQUATION Non Exact Eguation (xy + 1) dx tx (* + 4y - 2) dy - 0

A:

Q: Find the particular aolution of the differential equation with the initial condition given below.…

A:

Q: The differential equation (3ycosx+ 4.xe* +2x'e" dx+ 3(sin x+1)dy 0 is exact because OM ON Ox

A:

Q: Use separation of variables to find the general solution of the differential equation. dy 5x2 + 7 dx

A: Given:

Q: y" – 2y' + y = Ita² 1+x?

A: We use the method of variation of parameters

Q: dy 1. da + Зу 3D 2ге 2xe-3r du

A: Using differential equations.

Q: use the fact that 5x^2 - y^2 = c is a one parameter family of solutions of the differential equation…

A:

Q: The general solution for the flowing differential cquation is * (3x+ycosx) dx +(sinx-4y )dy =0

A: We will split the equation into separate differential forms and then integrate accordingly to get…

Q: The differential equation 3y(x -1dx+(x³ +8y– 3xdy = 0; is exact because OM ON %3D

A:

Q: A second-order non-homogeneous differential equation is given by d2y/dx2 − 10 dy/dx + 21? = 21x2 +…

A:

Q: O y"+y= secx cosecx %3D

A:

Q: x dy + y dx = 3x²y² dx, y(-1) = 2

A: Rewriting given differential equation into standard form of bernoulli equation

Q: d³y . 4 dx3 -13 + 6y = 0 dy dx

A: We have to solve given problem:

Q: gmmuany. Solve the differential equation d²y + 4y = 4tan2x by the method of variation dx2 of…

A:

Q: dy 2. dx 2y = x°y?

A: Using method of Bernoulli Differential equation.

Q: (х5 +3у)dx — хdy —D 0

A:

Q: What is the particular solution to the dy dx 4y differential equation 4 = with the initial condition…

A:

Q: Solve for the general solition of the followimg differential equation using FOLDE or FOBDE. 3. dy/dx…

A:

Q: 8. dy + ()y y dx = x* dx; y(0) = 2 2Vx. %3D

A:

Q: (D² – 2D + 5) y = 25x² + 12

A: Given: D2-2D+5y=25x2+12 So,  The auxiliary equation is: m2-2m+5=0 Now solve; m2-2m+5=0m1,…