A. y"-2y'+y=0 B. 2y"+5y'+3y= 0 y(0) = 3, y'(0) = -4 %3D %3D

Q: (a) (e* +In (y ))dx ++1 dy = +1 dy = 0 , y (In (2)) =1

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Is differential equation (4xy + 3y4)dx + (2x² + 5xy³)dy = 0 exact? If it is not exact what is its…

A: Given differential equation 4xy+3y4dx+2x2+5xy3dy=0. Is the differential equation exact? If not find…

Q: Find the differential dy for the given values of x and Δ x. y = 5x 2 - 2x + 3 ;  x = 2 , Δ x = - 1…

A: Given that: y=5x2-2x+3,  x=2  ,  Δx=-16

Q: Which one is an integrating factor for the equation y(2x – y+ 1)dx + x(3x – 4y+ 3)dy=0? 9020900 et

A: Given that, y2x-y+1dx+x3x-4y+3dy=0                               ……(1)   The above differential…

Q: Consider the homogeneous ordinary differential dy equation x dy 3x dx + Зу — 0, х>0 X > 0 - dx? with…

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Q: a- If w = x² + 2xy and x, y change from initial values (x = 1, y = 3) By amounts dx = 0.01 and dy =…

A: Given: w=x2+2xy So, dw=2x dx+2y dx+x dy...(1)

Q: The differential equation dx/dt = 100x(x- 5)+ s models a population with stocking at rate s.…

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Q: 1. Find the antiderivative a) S(eš* – ) dx b) Se-4*dx c) S Vx(2 + x²) dx d) S-2xe10 - x² dx e) S…

A: (a) Given that,

Q: Reducible to Exact (2xy ln y)dx+(x2+y2√y2+1)dy=0

A: We have: M = (2xy ln y)dx ∂M/∂y = 2x(1 + ln y) N = (x2+y2√y2+1)dy ∂N/∂x = 2x

Q: 1- xy dy + (x² + y² )dy = 0 dx 2- 2. dy – y = ex/2 3- (x + 2y)dx – xdy = 0 dy 4- cosh x+ (sinh x)y =…

A: As per the guidelines we can solve 2 problems.

Q: What is the rate equation for related to mixture problem? dx = r.c. + r;c; а. dt dx b. = r.C; - r;C.…

A: To find the rate equation related to the mixture problem.

Q: Find the eneral integration of th following differential equation xy-Y Xtan y x

A: Concept: Homogeneous differential equation: By integrating the provided differential equation, the…

Q: 3X An integrating factor for the DE dy + ydx = e³*dx 5 O ey O y O ex O x?

A: For a differential equation of the form, , the integrating factor is defined by .

Q: 4. Integration by Inspection y (2xy+ y²) dæ + x (y² – x) dy = 0

A: Differential equations

Q: Find the differential equation for the family of parabolas with axis parallel to the x-axis and with…

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Q: y_x + y х х — 1 dx

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Q: eny x+9 dx dy e+y en8 Iny dy %3D en8 e [ e-e] dy eny en8 [ye- e° ] dy | ل ام مو ] en8 | ye- e° - e ]…

A: Let…

Q: 10. The integrating factor of the FOLDE y'-2xy x is e^(-x^2) I am Sorry !!!!

A: The given differential equation can also be written as dydx-2xy=x Since it is a first-order linear…

Q: 4. x2 (In x - In у) dy 3D у (ylny— ylпx) dx

A: Solution

Q: The integrating factor of non-exact differential equation (x°y° – x° )ax – (y° – x°y)aY = U ,5, 1 x7…

A: We have the non-exact differential equation x3y3-x6dx-y6-x5ydy=0 This is a non-exact differential…

Q: 1. Solve the equation (x – y In y + y In x)dx + x(In y-In x)dy 0 using the method for homogenous…

A: Please see the answer below.

Q: The non-exact differential...(x² + y²)dx + (3xy2 + 2xy + x³)dy = 0 can be reduced to exact after…

A: We need to determine the integrating factor for the differential equation: x2+y2dx+3xy2+2xy+x3dy=0…

Q: 1.(x fan y t y) dx - xdy = 0 2- ye "dx - (ure)dy cbssitication and Solution by appropiate methed

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Q: dy 1; find dt dx at x =- dt Related Rates: Given y = cOs x + sin and 4

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Q: Is 1(y^2) is the integrating factor of the non-exact DE[(y^2)-y]dx+xdy=0, show your solution.

A: NOTE: Refresh your page if you can't see any equations. . compare this equation with  so here we…

Q: зхе-МХxcos(Nx) 5- a. Differentiate: y = M csc(Nx)+Nx

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Q: If µ(x, y) = x" y" is an integratingfac. of the the DE. . (1 + 3xy)dx + (xyl + x²)dy = 0 Then, the…

A: A differential equation of the form Mdx+Ndy=0 is said to be an exact differential equation if it…

Q: dy 1- dx e¯x-y-2 y(0)= -2 %3D dy 2- dx ylny %3D 1+x2 y(0)=e²

A: 1. ddxy=e-x-y-2,   y0=-2A first order separable ODE has the form of Ny·y'=MxRewrite, we get eyy'…

Q: Given a differential equation xy'+y = (xy) In x with initial an 1 condition y(1)=;. Calculate the…

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Q: Find the integrating factor: x^2 dy+(2x^3 y-e^x )dx=0

A: First order linear differential equation of the form dydx+P(x)y=Q(x) Integrating Factor:…

Q: 1. Find the general antiderivative. A. S 5x8 4x4 + 10x3 – x² – 9x + 15 dx В. /2 - cos x + sec x ·…

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Q: Show that the DE (4y3 -6xy)dy = (3y2 +2x)dx is exact and find a solution of the IVP: (4y3 - 6xy)dy…

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Q: Solve [y (In x – In y) + x] dx +a (In y – In a) dy = 0 xlny + yln x = Cx None of the choices ylnx +…

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Q: Find the differential equation of a family of parabolas with an axis parallel to the x-axis. O y"y –…

A: Option A

Q: Obtain the differential equation of the family of straight lines with slope and y-intercept equal. A…

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Q: 1. How many stable equilibria does the following autonomous differential e y' = y³ + 4y² + 4y

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Q: (2y° + xy }tx + (x*y² – 2}ty = 0 Integrating factors found by inspection: %3D

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Q: Obtain the differential equation of the family of curves, parabolas with vertex and focus on the y…

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Q: (x – y ln y + y ln æ)dx + x(ln y– In x)dy = 0 - - %3D

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Q: The equation (y-x)=x(dy/dx) is Bernouli (y^n> 1) O linear in x O Homogenous O variable separable

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Q: is 1/(y^2) is the integrating factor of the non-exacr DE[(y^2)-y]dx+xdy=0, show your solution.

A: Given: y2-ydx+xdy=0 So, M=y2-y ; N=xNow,∂M∂y=∂y2-y ∂y=2y-1∂N∂x=∂x∂x=1 As we know that the expression…

Q: x- y arctan (2) dx + x arctan () dy = 0

A: Given:  The given equation is    [x-y arctanyx)]dx+x arctan(yx)dy=0

Q: dy Find y(0-2) by using Euler's method for y=1 for x= 0. log10 (x+y) with initial condition %3D dx

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Q: 1. Given y = 4e* + In x, find the differential dy.

A: See the attachment

Q: The integrating factor of non-exact differential equation (z°y – x°)dx – (y – a³y)dy= 0 | %3D 1 x*y…

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Q: Find the value of the differential dy for y = e7x + 2x if x = 0 and dx = 0.1.

A: d/dx(e^(mx))=m e^(mx)

Q: (b) Evaluate 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y =…

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Q: Find the differential equation of a family of parabolas with an axis parallel to the x-axis. O y"y"…

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Q: = x²y - 1.1y dx using (a) analytical method, (b) 3rd-order to 5th order RK Method with h = 0.25 and…

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