. Find a general solution for y" + 4y = x² by method of undetermined coefficient

Q: xarctanydx + dy = 0 2(1+ y²)

A:

Q: Find the particular solution of 3x ydx – (x + y)dy = 0 y(1) = -2.

A: 3x2ydx-(x3+y3)dy=0M=3x2yN=-x3-y3My=3x2Nx=-3x2Since My≠NxTherefore, Non Exact diff. eq.Find…

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

A: Solution is given below:

Q: 5. Find a general solution to the Cauchy-Euler equation x?y" + 7xy' + 9y = 0, for x > 0.

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: Find the general solution of the following DE. xy(y')² + (x² + y²)y' + xy = 0

A: Here given the differential equation as xyy'2+x2+y2y'+xy=0 Replace y' by p, then xyp2+x2+y2p+xy=0…

Q: a. My =n xyy

A:

Q: Obtain the general solution. xy3dx+ex^2dy=0

A: The given differential equation is xy3dx+ex2dy=0. We have to obtain a general solution.

Q: Find the particular solution of y' = xey-x? given y(0) = 0.

A:

Q: Give a particular solution for y"– 2y' + y = ; ex 1+x2

A:

Q: Find the general solution of y’ + (1/3)y = exy4

A: We have to find the general solution of the differential equation y'+13y=exy4 .

Q: Find the general Solution of DES: x yy'= x +3y

A:

Q: Find the general solution or particular solution of each of the following D [1+ ytan(xy)]+…

A:

Q: - Employ Picard's method to obtain y (0-1) of the equation ay = x +y, given that Y, =0 when x, = 0.

A:

Q: Solve the non-homo. D.E. 1.y" + у%3D Зе2x

A: Differential

Q: 3. Find the particular solution of the differen- tial equation: (x² +y² )dy=xydx, given that x=1…

A:

Q: Find the general solution to y" – xy' = 0. -

A:

Q: Find a second solution to 4x²y" +y = 0, given one solution y1(x) = x!/² In x.

A: Given differential equation 4x2y''+y=0.....1 And given one solution is y1x=x12lnx Equation (1) can…

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

A:

Q: Use undetermined coefficients to find the particular solution to y'' - y = 4e t Y(t) =

A:

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

A: We will find out the required general solution.

Q: Let y(x) be the solution for the DE : У 3 (х +у-1)2 If y(0) = 1, then find y() 8 - JT JT Зл 4 Зл -…

A: Here to solve the given differential equation first we change the variable y by a  transformation .…

Q: Find a particular solution for: y" - 3y' + 2y = te*

A:

Q: Find a particular solution to y" + 6y' + 9y = 3z e

A: We use the method of variation of parameters to find the particular solution to the given…

Q: Use the variation of parameters to find the solution to the IVP. 0 1 et 1 X' (t) = x(t) + ,and X(0)…

A:

Q: The general solution of the DE: -y = 1 is y= x(x + c)

A: given,1xy'-1x2y=1multiplying throughout by x we gety'-1xy=xnow, integrating factor μ(x) is given…

Q: 12. Find the general solution of x²dx + y(x – 1)dy = 0

A: This is a variable seperable DE.

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 3e* Y,(t) =|

A: The given differential equation is  y"-y'-6y=3e3t  We have to find the particular solution of the…

Q: 2x Find the general solution of y" – 4y' + 5y sin (2)'

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

Q: x²y" +xy' – 4y = 2x*

A:

Q: Give a particular solution for y" – 2y' + y = ex 1+x2

A:

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: Find the general Solution of DES x y = xy +y

A: Given:    x2y' = xy + y2

Q: Find the general solution of the given DE. y"-2y"-y'+ 2y 0 %D

A: NOTE: Refresh your page if you can't see any equations. . the auxiliary equation is given by

Q: 4. Find the complete solution of xdy + (x³ – xy? – y)dy = 0 |

A: According to question,Given differential equation,x dy + x3 - xy2 -y dy = 0

Q: Show that y = In (x) is a solution of xy" + y² = 0.

A:

Q: Obtain the general and particular solution 4. xydx + (x² + y²)dy = 0

A: The given problem is solved below in detail.

Q: Solve the given problem: y'' + 4y= 3sin2x

A:

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

A:

Q: Obtain the particular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1

A:

Q: -Find the solution of y"+y' + by = 0 by transforming y = x"u|

A: Put y=xαu in the given equation y'=xαu' y"=xαu" Then the equation becomes xαu''+axxαu'+bxαu=0 Now…

Q: Obtain the general solution using the method of undetermined coefficients.(D^2 + D)y = − cos x

A:

Q: Use undetermined coefficients to find the particular solution to y''−9y'+20y=−1768sin(t)

A:

Q: (b) Find the general solution of: əz = yx² - xy Əx Given z = y when x = 1, determine the particular…

A:

Q: Find the general solution of the DE below. y(1) + y “ + y“ = 0 יינ

A:

Q: 2. Determine the general solution of y(") = x- 2y cot (2x)

A:

Q: Find the general solution of the following DE. xy² (y')² + y(x - 1)y' - x³ = 0

A:

Q: (b) Find the general solution of: = yx² - xy ax Given z = y when x=1, determine the particular…

A:

Q: Find the general solution of y" + 2y=ex +2.

A: The Auxiliary equation is D2+2=0 solve for D Therefore  D=±-2=±2i Therefore the solution is…