solve the following D.E ,t<3 y" – 3y - 4y =- , y(0) = 0, y'(0) = 0 : ,t23

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

A: We have to solve given problem:

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y' = y2/√x and y(1) = -1.  What is the exact…

A: In the given question, it is asked to solve a differential equation using Euler’s method.

Q: Solve using Euler's Method dy dx sin(x+y) ex,y (0)-4, h-0.1 -

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Q: 18. y = x/I - x?

A: Differentiation:- The derivative of a function of real variable measures the sensitivity to change…

Q: 2(y+1) dy t 2) 2(у + 1)4 dx x+1

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Q: Solve the differential eqyations (3x +5y +4)dx + (5x +3y +6)dy =0

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Q: Given the differential equation of the family of circles with radius of 2 units and whose center's…

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Q: Let y tan(5x + 8). Find the differential dy when I = 5 and dr 0.1 Find the differential dy when I 5…

A: y=tan(5x+8)Differentiate on both sidesdy=sec2(5x+8)×5×dxSubstitute x=5  , dx=0.1…

Q: find particular solution of (16x+5y)dx+(3x+y)dy=0. If the curve to pass thru the point (1,-3)

A: Given: 16x+5ydx=-3x+ydydydx=-16x+5y3x+y               It is a homogenous differential equation.…

Q: Use the Euler method with dx = 1/3 to estimate y(2) if y' = y - e2xand y(0) =1.  What is the exact…

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Q: 5.32. z = sin(x² + y?)

A: To find the differentials of third order.

Q: Find the general solution of 2ydx + (x – sin Jy)dy = 0.

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Q: Use the differential dy to approximate Ay when x changes from x = -3 tox = -2.99. y = x2 + 1 Enter…

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Q: dy Find the particular solution of 2y- = x+ sin a when y (0) = 1

A: we have to integrate both side , we get

Q: A particle moves along the x-axis with velocity given by v(t) = 67 sin (at) for time t> 0. If the…

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Q: 2, t'y"+ty'+y= Cos(int)

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Q: Solve 12 dy dy ty = t®y=1 dt

A: A differential eqaution of the form y'+p(x) y=q(x) yn, n ∈ℝ is called a Bernoulli differential…

Q: (solve exact de) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xye )dy

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Q: )L{sinh(7t) + (2t + 1)U (t – 1)},

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Q: 3. Determine the Particular solution of this equation In terms ofY (xy2)dx + e*dy 0, as x → 0, y ==

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Q: fy = f(r), how do we define the differential dy

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Q: 1. If y"+y= 2x + 3e* then the roots of equation, r₁=. 12 = lyp= = second order differential equ and…

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Q: A particle moves along the x-axis with velocity given by v(t) = 6T sin (2nt) for time t > 0. If the…

A: Given: vt=6πsin2πt at t = 1, x = -4

Q: 9. Find dy for y defined implicitly. by the equation xy-secly)-3x

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Q: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

A: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

Q: Find the differential dz of the function f(x, y) = 4y² + x²y-2xy and use it to approximate Az at…

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Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - dy -x-(x2+y²). sec.…

A: Please see the explanation below..

Q: Solve the equation xcosy dy+(x+2)siny dx=0.

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Q: Find the differential dy. y = cubic root of 3x^2

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Q: Find the differential dy for y = xV1-x. Do not simplify your answer.

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Q: II. Solve th following DEs by LT. 1. y" + 2y' – 3y = sin(2x), y(0) = y'(0) = 0 %3D -

A: We are given a linear second order nonhomogeneous differential equation with constant coefficients…

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

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

Q: Find the general solution analytically: (dy/dx) = 4 - y

A: Given data: The given differential equation is (dy/dx)=4-y. The given differential equation can be…

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

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Q: ædy – y(1+ In y – In æ)dx = 0

A: The given differential equation  is changed to  the variable separable form by using the…

Q: ve the given differential equati dy dx - (1 + x)y = xy

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Q: dy + ytanx = y° sec° x dx

A: We have to solve given problem:

Q: ydx = x(1+ xy4)dy

A: Given ydx=x(1+xy4)dy ⇒dxdy=xy+x2y4y⇒dxdy+x-1y=x2y3

Q: Find the differential dy of the given function. Xx + 5 y = 2х — 9

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Q: A particle moves along the x-axis with velocity given by v(t) = 3T sin (t) for time 10 at time t =…

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Q: Q:: If In/x2 + y² =sec(), use implicit differential to proof the following: - -x-(r+y?). sec. tan…

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Q: I. Find dy/dx in the following: 6. Y=sec² Inx

A: We are given: y=sec-1 lnx The derivative can be found as follows:

Q: Find the general solution of the equation dy + (tan t) y = cost dt

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Q: If y = 5x2 + 2x + 9 , find the value of the differential dy as x changes from 3 to 3.1

A: Given, y = 5x2 + 2x + 9Differentiating with respect to x;dydx = 10x + 2At x = 3, dydxx = 3 = 10×3 +…

Q: Find the differential dy of the given function. y = √(9 − x2)

A: The given function is Now, find the derivative of the function

Q: Find the differential dy for the function y=3sin(2x)+x.

A: We have to find dy for the function y=3sin(2x)+x.

Q: Solve for the general solution of the given non-exact DE. y(y + 2x – 2)dx – 2(x + y)dy = 0 - -

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Q: Find dy/dx at the given point without first solving for y. x2 — бу — 37 %3D0 at (1, -6) | dy dx

A: This question is based on derivative.

Q: Solve for the general solition of the followimg differential equation using FOLDE or FOBDE. 3. dy/dx…

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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.