Solve ởy ôt y (x, 0)= 3 sin 2n x, y (0, t) = 0 = y (1, t); 0 0. %3D ốt

Q: dx xt x(1) = 2, solve for x(2) when h = 0.1 %| dt t²+2

A: As per the question we have to solve the following first order differential equation : dy/dx =…

Q: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

A: Solve using integrating factor by inspection: (x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0

Q: Obtain the particular solution of the DE: 4(3x + y – 2) dx – (3x + y) dy = 0; when x = 1, y = 0…

A: Gg

Q: Inx dx, 2. Integrate (1) using the substitution u = In x (ii) using integration by parts.

A: Integration by substitutions and by parts

Q: Solve the homogeneous DE 3xy dx + (x^2 + y^2) dy = 0.

A: We will take the substitution y=vx, to convert it into separable variable form.

Q: Solve the homogeneous DE. 3. (x – y sec?2 – x tan2) dx + x sec² 2 dy = 0 -

A: Given that: x-ysec2yx-xtanyxdx+xsec2yxdy=0

Q: Q1. Solve the IVP by finding appropriate integrating factor an (x² + y² – 5)dx – (y + xy)dx = 0,…

A: Consider the given differential equation Mdx+Ndy=0 The equation is exact if ∂M∂y=∂N∂x The solution…

Q: Solve ODE for general solution: (2ysin(x)cos(x)-y+2y^(2)e^(xy^2))dx=(x-sin^2(x)-4xye^(xy^2)dy

A: Hence the given ode is exact. Obtain the general solution as follows,

Q: (b) Solve the integral [(3x – y)dx +(2x +3y)dy along the curve x = y' from (0,0) to (1, 1).

A: Solution of question as follows

Q: Let y 5x? + 5x + 2. || Find the differential dy when x = 5 and dx = 0.3 Find the differential dy…

A: GIVEN: y = 5x2 + 5x + 2

Q: y' cos x + y sin x = 2cos³x sin x- 1 What is the particular solution when y(T/4)=3v2 ?

A: Given differential equation is y'cosx+ysinx=2cos3xsinx-1 we have to find the particular solution…

Q: The integrating factor of the DE   y(2x - y + 1) dx + x(3x - 4y + 3) dy = 0 is

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Q: Solve the given initial-value problem by finding an appropriate integrating factor (x + y - 5) dx =…

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Q: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy - y = 0 dx + x + 4y dt — 10%; х - | dt

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Q: A. Integration by parts o (3t + t*) sin(2t) dt

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Find the solution asked using the process of Homogeneous. (16x + 5y)dx + (3x + y)dy = 0; the curve…

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Q: (ii) o S(2xy + z)dx dy dz z=-1 :0 Jx=1

A:

Q: (. 0) S(x, y) = In(x² + xy), at (4, 1) S(x, y) = sin (x²) + cos y, at

A: 19. f(x, y)=sin(x2)+cos y At π2, 0, fπ2, 0=sinπ22+cos 0                =sinπ4+cos 0…

Q: What is the integrating factor of 2 (y – 4x²) dx + ædy = 0? | Oe O 2r

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Q: COS f(2, Y) af af dy f(x, y) = log, (3x) af %3D fe dy

A:

Q: What is the integrating factor of y (x² + y) dx + x (x2 - 2y) dy = 0? -1

A: We will find out the required integrating factor.

Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sinh (xy - z2)

A:

Q: Solve using homogeneous differential equation x*dy+(2.xy – y² kdx = 0 Let the substitution y=2;…

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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: Test for exactness and determine the particular solution of: (yexy – 2y³)dx+ (xexy – 6xy2 – 2y)dy =…

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

Q: Solve for the general solution of the given DE by using the integrating factors found by inspection.…

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Q: Solve using homogeneous differential equation y'dx- (xy + y° kty = 0 Let the substitution y=? 2;…

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Q: 4. y? cos x dx + (4 + 5y sin x )dy = 0

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Q: find ƒx , ƒy  . 1.ƒ(x, y) = e^(xy) ln y 2. ƒ(x, y) = cos^2 (3x - y2 )

A: Hi! You have uploaded multiple questions. As per norms, we will be solving only the first question…

Q: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

A: Given: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

Q: (xy+2)dx+(§x*y+8x-4y* )dy =0

A:

Q: 3. Show that the DE is not exact, determine the integrating factor, make it exact and solve. a. (2y…

A: The given differential equation is…

Q: Use Euler's method to approximate the solution of the IVP, yx? – 1.2y, y(0) = 1 on the interval [0,…

A: Euler's method: Euler's method is used to find the approximated solution of first order differential…

Q: solve using the method of integrating factors. dy dx ==+x, y(1) = 3 х ||

A:

Q: Solve the differential equation by separating method dy = (3x? +1), dx (2y –1) given x =1 when y = 2…

A: Method of Separation of Variables (for First-order  ODE) : If the differential equation is of the…

Q: h of the DE's =)y = 2 sin² x ; y(0) = 0 , y'(0) =-2

A:

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: Solve the differential eavations ydx xdy = 0 x' +y° +y?

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Q: "ind general solution for dy dy + 3 + 2y = -20 sin 2t, y (0) = 2, y' (0) = 1. dt2 dt

A: Ode

Q: the initial value DE y' - ytanx = sinx, y(0) = 1 cos 2x 5-cos 2x %3D 4 sin x 5-cos 3x 5-cos 2x В) у…

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Q: Pydx + x(2 + x²y) dy = 0

A: Topic:- differential equations

Q: Solve the differential equatic y' = (x + y + 2)², Chart Area y(0) = 2 by setting u = x + y + 2.

A: y'=x+y+22let u=x+y+2     u'=1+y'     y'=u'-1

Q: dy/dx=x2+3y2/2xy

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Q: dy Use integration to find the general solution to the differential equation: dx sec(y) %3D (x – 1)2

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Q: Solve the DE by Integrating Factors 1. y² dx + ( 3xy + y² - 1) dy = 0

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Q: (b) Solve the integral (3x– y)dx+(2x+3y)dy along the curve x = y' from (0,0) to (1, 1).

A: