En(x,y) be a basic solution of the Laplace equation. and x is fixed point in R^n. Let L() be the distribution (on the Schwartz space) corresponding to the function En(x,*) །།། ། ་་ Find all distributions (on the Schwartz space) Z that satisfy the equation (AL() = x(): AZ(·) — 4Z(·) = ½-½³x(·) — 2L(·), where delta(x) is the Dirac delta at point x (reminder delta(x) = DELTA(L())

Q: Identify the type of the equation dy y? - dx and solve it.

A:

Q: Solve the following differential equations using power series y" – (x² – 1)y + y = 0

A: Given differential equation is y''-(x2-1)y'+y=0                               (1) using power series…

Q: %3D

A:

Q: 6. (x² + y²) dx + xy dy - x = 1 C= Ja y = 2 or 9 O= √3

A:

Q: 4. y(4) + 17y" + 72 = 0.

A:

Q: 2) Solve the differential equation y' + y? + (2x + 1)y+ x² + x + 1 = 0.

A: This will be solved by substitution of x+y =z ,here is the solution.

Q: 3 Solue Cy+2*g³)dx + C2+3x' (2+ 3x*;'+ x) dy=0

A:

Q: Find the solution of the differential equation (1+x* )y'+2.xy – 4x°y° = 0 (Bernoulli) %3D

A: We will find out the required general solution .

Q: (sin t)y' - (cost)y = 4t(sin² t), 0<t</

A:

Q: (e"siny + tany)dx + (e*cosy + xsec*y)dy = 0

A:

Q: ELIMINATE THE ARBITRARY CONSTANTS y = x² + ax + be¯*

A:

Q: solve the differential equation: (3y ′′ + y ′ − 14) = 24e^16 − 48 (Explain the summary of steps…

A:

Q: 2) Solve the equation y' = Y 4x²y + x

A:

Q: (7 dy dx X = 0 = y - xy³² y = 21/12/2 -2x Answer: G = 17

A: We use the Bernoulli differential equation concept to solve given differential equation.

Q: 1. 7ху' — 2у + (E) - = 0

A: Given differential equation  7xy'-2y+xy6=0

Q: the appropriate that should be applied the differential equation 4 - 54 - 5 xyở ³ 2 K

A:

Q: Find a general solution of the differential equation: x²y" – 3xy' + 4y = 2x -

A:

Q: y' + y secx = 1

A: We have to solve the following 1st order differential equation…

Q: 1) y" - 4y = e², y (0) = 0, y' (0) = 0

A:

Q: Apæ'/s-1/Apy/s-1 %3D

A: The given equation is: xy=λρx1s-1λρy1s-1

Q: Solve the nonhomogeneous opdr – 2rdo = q' In odo. equation

A:

Q: 3. (x + y - 6) dx + (x -y + 4)dy = 0.

A:

Q: Solve the equation y' + y cot x = y* sin x.

A:

Q: y'+9xe"+3* = 0 y+3x

A: We use method of Variable separable to solve this differential equation

Q: show that the inverse of arotation matrix is transpose,which is also arotation matrix, and it is…

A:

Q: Solve (D² + 4D + 5) = 0 ,y(0) = 1 ,y'(0) = 0. %3D

A: Differential equation

Q: 1=6 | = X x + ₂ ht ₂ x 1 + x) dx + xydy = 0

A:

Q: xy' + (1 + x)y = e* sin 2x %3D

A: xdydx+1+xy=e-xsin2x

Q: 2y" + 3y' + y = x² + 3 sin x

A:

Q: Solve y" – 4y' + 4y = 6xe2".

A: