A Q2 Show that y=x+ is the solution of 3x – x = x+ y. dy dx

Q: Find the solution of the DE using variation of Parameters y''' - 3y'' + 3y = (ex/x)

A: The given problem is to find the solution of differential equation using method of variation of…

Q: Obtain the particular solutions of the following: (y-Vr² + y² \dx– xdy =0, y(0)=1 a.

A: Solution is given below:

Q: Find the solution of y- dy --x = 0 using separable variable method. dx +C 2 3 Ob. None of these y +C…

A:

Q: Find the general solution of: y(x°+x*)dx - x(x³+ y-)dy = 0

A:

Q: 4. Find an implicit solution using the substitution u= or y3ux dy dx x+xy %3D

A:

Q: The general solution of (2x2 + y) dx + (x²y – x) dy = 0 is 4x2 + Dy² -Dy D

A: Given that 2x2+ydx+x2y-xdy=0Solution…

Q: 3. Find the complete solution of 2xdy – y(x + 1)dx + 6y³dx = 0

A:

Q: 2. Find the general solution to d²y dz² dy + 3y = e* dr

A:

Q: a) Find the general solution for UTM dy TM dy +2- dr? dr (1+f) UTM (77 +1)xz² = fip +

A:

Q: Find the general solution of using the method of variation of parameters. d²y dy 2- - 42+ 2y = xe 2x…

A: Given,2y"-4y'+2y=xe2xComplementary SolutionAuxiliary Equation is 2m2-4m+2=0⇒m2-2m+1=0⇒m-12=0⇒m= 1 ,…

Q: Obtain the general solution. (Let 2C=C) (4x + xy*)dx + (y +x*y)dy = 0

A:

Q: fin the general solution of (x+2y-4)dx - (2x+5-y)dy=0

A: Please see the below picture for detailed solution.

Q: Find the particular solution to D²y – 6Dy + 9y = e3x – ex when x = 0, y =y' = - 3 %3D

A: For given differential equation we have to find particular solution.

Q: Find the particular solution of -4y = 3x – 1 given that when x=0, y=0 and d2x dx dx II

A:

Q: (r²+y + y³) dx – x dy=0

A: →∫1a2 + x2dx  = 1atan-1xa→ddxuv = udvdx + vdudx

Q: Find a particular solution to y"+2y' + y =t

A:

Q: Show that the solution of the equation d3y/dx3 +3αd2y/dx2 +3α2dy/dx+ α^3 y = 0 is y…

A: According to the given information, First it is required to show the solution of given differential…

Q: Obtain the general solution. 1. y' = xy?

A: We will find out the required general solution.

Q: Find the complete solution of the DE (D3+6D2+11D+6)y=ex +cosx.

A:

Q: Obtain the general solution unless otherwise instructed d²y 1. dx2 - y = 10sin²x

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: (y+x*y²) dx +x dy = 0 5.

A:

Q: If find the value of a. 3 S₁ S² (x + 2y) dydx = 10, 0 a

A: Given: ∫01∫a3(x+2y)dydx

Q: a) Give a particular solution for y" – 2y' + y = 3e*. %3D

A:

Q: SOLVE THE EQUATION (y -2) dx - (x-y-Ddy = o ISSING THE DE LINEAR IN x 4 Y VAKIABLES.

A:

Q: dy 3. Solve dx = -8xy² +4x(4x+1)y-(8x' +4x² -1) by knowing u = x is a solution.

A: Given differential equation is dydx=-8xy2+4x4x+1y-8x3+4x2-1             …(1) y=x is a solution of…

Q: ind the particular solution of (9x-2yldx- x(6x- yldy-0 when x-1. y=1 To start let y-vx

A:

Q: x²dx + y(x-1)dy = 0 %3D

A: We need to find solution of differential equation.

Q: Solve the IVP y + 2y = 0 if t≥ 1 y(0) 1. Is the solution continuous? = "

A:

Q: what is the general solution of d^3x/dt^3 - 19 dx/dt + 30=0

A:

Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: Use the method of variation of parameters to solve the following y + 4y + 4y e- In z, z>0

A:

Q: 2. Find the general solution of d²y dy +5 dx² dx -6y= = : 0

A:

Q: Show that the solution of the equation d3y/dx3+3αd2y/dx2+3α2dy/dx+α3y = 0 is y = (Ax2+Bx+C)e−αx.…

A: Explanation of the solution is given below...

Q: Find the general solution of (2x – y) dy = 2y – x - da

A:

Q: Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are…

A:

Q: 3. Obtain the general solution of: (x – y)(4x + y) dx + x(5x – y) dy = 0

A:

Q: (D* – 4D³ +14D² – 20D +9)y = 0 - -

A:

Q: (i+z) dy 3. Solve (itx) 9

A:

Q: (D³ + 2D² − 5D − 8)y = 0, when x = 0, y = 0, y' = 0, y = 2 - -

A: Given  (D3+2D2-5D-8)y=0 and when x=0, y=0, y'=0, y''=2. The formula for differentiation is…

Q: 3. Find the general solutions of, dy_x+y dx х-у, а.

A: given differential equation is  dydx=x+yx-y

Q: 3. Find the general solution of dy = y(xy – 1). d:r

A:

Q: dy Find the solution of = y (8 – ) satisfying the initial condition y(0) = 144.

A:

Q: 2. Find the general solution of d³y dy dy 6- dr3 + 12 dx2 dx 8y = 21e2 -

A: To find- Find the general solution of  d3ydx3 - 6d2ydx2 + 12dydx - 8y = 21e2x

Q: Show that xy – 2 = cxy is a solution of (x² + y2 – x)dx – ydy = 0.

A: Given  x2+y2-xdx-ydy=0 dydx=x2+y2-xy

Q: olve the initial value problem by standard method  (x^2+3y^2)dx-2xydy=0,  y(2)=6

A: We need to solve differential equationx2+3y2dx-2xydy=02xydy=x2+3y2dxdydx=x2+3y22xy

Q: Fınd the general solution of d²y dy + 2x - 2y = 0 dx dx² where y(x) = x is a solution.

A:

Q: OBTAIN THE GENERAL SOLUTION (x - 1) dx - (3x - 2y - 5) dy = 0

A:

Q: (D³ + 2D² - 5D - 8)y = 0, when x = 0, y = 0, y = 0, y" = 2

A: Given