H.W: show that the equations are homogeneous and solve: 1. (x + y)dy + (x- y)dx = 0 2. x*dy +(y - xy)dx 0

Q: Solve the general or particular solution for the following homogeneous equations. (8x − y)dx + 6x…

A:

Q: 5. Solve the higher-order Homogeneous D.E. y"" + 2y" + 9y' + 18y = 0 6. Solve the goneral coluti

A:

Q: t2 + y? = ty dt

A:

Q: Which of the following is a homogeneous equation? y (x'e*y) dx + x (y + x'e*y) dy O fkmb;lf None of…

A: Homogenous differential equations.

Q: Which of the following is a homogeneous equation? y (x'e*y) dx + x (y + x³e*y) dy .fkmb;lf O None of…

A:

Q: + (4xy – 3x²) dy = 0, find an integrating factor of the form d equation. %3D

A: First we have to find integrating factor for given differential equation and with the help of…

Q: Show that the equation is homogeneous and find its solution. dy/dx=x+y/x

A:

Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1)=Q %3D

A:

Q: Find an integrating factor and solve the equation у da + (3гy — e Sу) dy %3D 0. -

A:

Q: Solve the following homogeneous problem in general: + 22 Py dx? dy + x – y = 0 dx dr3

A:

Q: Which of the following is/are homogeneous equation/s? I.) 3y'' - 2y + 1 = 0 II.) 3 dy3/dx3 - 2…

A: Homogeneous equation : The homogeneous equation of the nth order with constant coefficient can be…

Q: b) Solve by using Runge-Kutta method to find y,. dy = x + cos(y) ; 0Sx<1 ;y(0) = 1; h = 0.5 dx

A: Solve the intial value problem, using Rung-Kutta method

Q: Solve the given differentlal equation by using an appropriate substitution. The DE is homogeneous.…

A:

Q: Determine the solution of the following homogeneous DE: sec (G) -y ]dx +xdy

A: Given differential equation is x secyx - y dx + x dy = 0

Q: (2y-x)(dy/dx) = 2x + y, given that y = 3 and  when x = 2 Homogeneous equations

A: Solve the following problem by substitution.

Q: 5.(y?dy) = x(xdy – ydx)ey

A: xexy(x dy-ydx)-y2 dy=0x2 exy dy -xy exy dx =y2 dyx2y2exy -xy exy dxdy =1dxdy=x2y2exy -1xyexy…

Q: For the homogeneous equation (y² + 2xy) dx -x²dy = 0, which is a better substitute: letx=vyory=vx?…

A: The given equation is; (y2+2xy)dx -x2dy=0.

Q: y² dx + x(x – 7y) dy = 0

A:

Q: Consider the DE d?y dy + - 6y = 12x, y(0) = 1 - dx? dx 1 is a solution of the DE and determine 3…

A: y=Ae2x-2x-13 Differentiating with respect to x, we get dydx=A·2e2x-21-0   ∵deaxdx=aeax, dxndx=nxn-1…

Q: Determine the linearity and solve for the general solution to the given DE * dx ecos y – x cot y dy

A:

Q: B. Solve the following equation using the determination of integrating factors. 2. y(4x + y)dx –…

A:

Q: Find the conditions such that the equation M (x, y) dx +N (x, y) dy = 0 is both homogeneous and…

A: We are going to solve

Q: (x-y)dx+(x-y+2)dy=0,Solve For Homogeneous DE

A: Given differential equation is (x-y)dx+(x-y+2)dy=0 Solve homogeneous DE

Q: Find the conditions such that the equation M (x, y) dx + N (x, y) dy = 0 is both homogeneous and…

A: We have to solve

Q: Solve the following DE equation dy/dx=y^2/2x - y/x - 4/x              y(x)=4  Riccati DE Eqaution…

A: Since you have asked multiple problems, I answered first one. If you need solution of other problem,…

Q: explan why it is always possible to express any homogeneous equation M(x,y)dy=0 in form dy/dx=f(y/x)

A:

Q: 5. dy 4y-3x 2x-y dx

A:

Q: Given that e" and xe" are solutions to the corresponding homogeneous equation, find a particular…

A:

Q: Solve the given problem Homogeneous (y? – xy)dx + (x²)dy = 0 on

A:

Q: consider this: (1+2xy3)dx+(3x2y2-(1/y))dy=0 A) is it Seperable B) is it homogeneous C) Is it…

A: Considering given differential equation, we have to find A) , B), C)

Q: solve the first order homogeneous  equation  dy/dx =y/x +(x/y) ^2 , given y(1) =2

A:

Q: Solve the homogeneous equation. (y^2 +2xy)dx - x^2 dy = 0 %3D ww w

A:

Q: determine the general equation; variable separable, homogeneous, exact, non-exact DE…

A:

Q: For the homogeneous equation y?dy = x(xdy - ydx)e"by, do the following: 1. Derive the integrable…

A: We have to find general solution.

Q: Given the DE: (5x - y) dy + (3x - 7y) dx = 0. 1. Show that the DE is homogeneous 2. Find the general…

A: Homogeneous differential equation

Q: Solve the given boundary-value problem. (If an answer does not exist, enter DNE.) y" - 2y' + 2y = 0,…

A: Given differential equation is a homogeneous equation with constant coefficient. We use auxiliary…

Q: Solve the given DEQS by using an appropriate substitution. a) xyy' + 4x² + y² b) (2х + у + 4)dx + (х…

A:

Q: d'y dx di y (x,0)=sin Tx ,t=0,0 ≤ x ≤l 8 dy (x,0) Solve the equation and with y (0,1)=y (1,r) = 0…

A:

Q: у? dx + x(х — 7у) dy %3D 0

A: Topic - differential equation

Q: Solve for the solution of the Homogeneous DE: (y + Vx2 +y?)dx – xdy = 0 when x = v3; y = 1 a. x? =…

A: homogeneous DE

Q: Solve the homogeneous DE. 4. y? dx + x(x + y)dy = 0

A:

Q: Find the conditions such that the equation M (x,y) dx +N (x, y) dy = 0 is both homogeneous and…

A:

Q: с. (х — 2у)dx + (у — 2х) dy %3D 0

A:

Q: Show that the following equation is homogeneous and then find the general solution. か_デー y -xy dx…

A: We have given differential equation ,  dydx = y2 - xyx2 - xy Here , fx , y = y2 - xyx2 - xy Now ,…

Q: 3. dy dx x² + xy + y² x²

A:

Q: Given that y1(t) = et, y2(t) = tet, and y3(t) = e−t are solutions of the homogeneous equation…

A:

Q: z = x+ y dy_ x + y +2 1. Using substitution change the dx x+ y+7 to a separable equation, Hence…

A:

Q: Solve the DE by Homogeneous Equation 1. x y dx + (x² + y²) dy = 0

A:

Q: Solve the DE: (1+ y?) dæ + (x²y + y) dy = 0 O Not Exact DE Exact DE

A:

Q: 1. dy x + y dx X

A: Solution :-