If u(x,y) =3x2y+2x2-y3-2y2, then u is harmonic %3D

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

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: Ans: (x + y)e+y = C y'+--2

A: Given differential equation is homogeneous differential equation which can be solved by converting…

Q: Find the Particular solution of the ODE d²y dy - 62-7y = -9e-2x, at y(0) = -2 and ỹ(0) = –13 dx2 dx

A: To find The particular solution of the given ODE.

Q: y"-uy'+5y= e Sin() %3D

A: We have to solve given problem:

Q: $5y dx + 4x dy,where C is the square with vertices (0, 0), (2, 0). (2, 2), and (0, 2) oriented…

A:

Q: Find the general solution of dy -2x6 dx y-4

A:

Q: Solve the Cauchy euler equation d³y x3 dx3 3x2 d?y dx2 2 + 6x -6y = 3 + Inx³ dy dx

A:

Q: The integrating factor (IF) of the equation: (2x³y + 4x<y + 2xy² + xy* + 2y)dx + (2y³ + 2x²y + 2x)…

A: Solution: Given: 2x3y2+4x2y+2xy2+xy4+2ydy + 2y3+2x2y+2xdy=0⋯⋯⋯⋯⋯⋯eq.1

Q: Employ Picard's method to obtain y (0-1) of the equation y,=0 when x =0. :=x² +y}, given that %3D

A: Given IVP is dydx=x2+y2, y0=0 when x0=0 Let f(x,y)=x2+y2 , y0=0 when x0=0. Formula for Picard…

Q: Find the general solution of (y² + 2y) sin æ²dæ + dy = 0. y+1

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Q: The general solution of x*y = -x³y- csc(xy) is A 2x^сos(xy) - 1 %3Dсх B 2x?sec(xy)+1= cx…

A:

Q: ....** ........* The equation y2 = cx constitutes an implicit general solution to the DE: %3D Select…

A: y2=Cxy2x=C differentiating  both side  dx-1y2dx=dcdx

Q: Obtain the General Solution of dx + xydy = y²dx + ydy.

A:

Q: В. NON-HOMOGENEOUS HIGHER ORDERED LDE 1. (D3 + 5D² + 3D - 9)y = 64x²e-3x 2. (D³ + 13D - 34)y = 25x2…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: - Find the solution of the equation 3U, -5U, = 0 satisfying the condition U(0, y) = sin y

A: We have to find the solution to the given equation.

Q: The equation 5z + zy = C is the general %3D Sz- 10 - A 10

A: The general solution of the differential equation: - A differential equation is an equation that…

Q: 1 Oy' = %3D xsiny+2sin2y

A:

Q: Find the general solution of: ydx — х*dy 3D0. || -

A: Use variable separable to solve the differential equation. Note: We are allowed to solve one…

Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: 1 dz, C:k – 3i] = 3 z² +4z + 13

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the solution of Uxy - x²y = 0, Uy (0, y) = y², u(x, 1) = cos(x)

A:

Q: Find the Particular solution of the ODE d?y dy -6--7y = -9e-2x, dx2 at y(0) = -2 and y(0) = -13 %3D…

A: We have to find the particular solution of the ODE                       d2ydx2-6dydx-7y=-9e-2x at…

Q: Solve the equation ru, + (x + y)uy = 1 %3D on dof:

A: In this question, we solve the partial differential equation by using characteristic method.

Q: Solve for the particular solution: dy + 를y3D -2°y"; y(-1) %3D2 dz

A:

Q: Transform the equation 2r (y + 1) dr form of variable separable. - ydy = 0 into the %3D 2adr dy y-1…

A:

Q: Find the general solution of 2y"+3y+y=3sin.x+xe"

A:

Q: 1. The complementary equation to dt² + dy + 4y = 5e-³t is:

A: Solution is here

Q: Solve the Cauchy euler equation d²y + 6x 2-6y = 3 + Inx3 dx x3 d3y 3x2 dx2 dy dx3

A:

Q: dy + ydx %3D = 3x²y?dx,

A:

Q: The particular solution of x dy - y dx when x = 1, y = 3 is a. y + x2 – 1 = 3x b. y + 2x2 + 1 = 6x –…

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Q: What is P-(y) if the given DE is xydx – (3y – x²)dy = 0? -2y 2y 2 y -2y-1

A: Given : Linear differential equation  Need re write in x form as follows dx/dy +P(y)x=Q(y)

Q: What is the annihilator for y=x e*cos 2x ? A (D2-2D+5)2 B (D2+5)2 © D2-2D+5 (D D2 +5

A: A detailed solution is given below.

Q: Solve the Cauchy-Euler equation: x*y' Зху + 4y = 0. %3D

A: Given Cauchy-Euler differential equation is

Q: The standard form of 3dy- xydx= 3y e* 4x/3 by Bernoulli's equation is: dx = 3e /3,3 ху A dy B y…

A:

Q: Obtain the general solution to the equation. dy y + 7x +1

A: Here we have to find general solution of differential equation

Q: (b) Find the general solution of (y* + 2y)dx + (xy³ + 2y* – 4x)dy = 0 %3D

A:

Q: Identify the Cauchy-Euler equation. O g- 52* + 8y = 0 dz4 22 y" – 7xy' + 6y = 0 O 2y" + 2a?y" – y' +…

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Q: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

A:

Q: What is the general solution of (y? – 3y – x) dx + (2y-3) dy = 0 %3D Oy-3y- c + 1= C 3y a 1== Ce*…

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Q: •ý -2ý +y= ě sinx %3D Ans: y=ě +2xě - ě sinx • ý -uý ruy = 12 /* %3D e 2X 2 ZX .2 +C2 X e + 20

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

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

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

Q: Find a general solution to the Cauchy-Euler equation x°y'"' - 8x²y" + 9xy' – 9y = x², x> 0,

A:

Q: Solve the follawing systen. 2 x, - 5x - cost dt dx2 b) by using the method of unde termined…

A: Given system is dx1dt=2x1-5x2-costdx2dt=x1-2x2+sint First, let us solve corresponding homogenous…

Q: The singular points for the D.E. (x² – 2x– 3)y" + 4xy' + 2y= 0, are:

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Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D. Answer:

A:

Q: The particular solution of y(x+ y)dx + (x+ 2y- 1)dy=0; y(0)= 2 by NEDE is

A: Let's find.

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y(-)= 3x²y² becomes A none…

A: We have to write the differential equation in terms of dz/dx.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.