Consider the differential equation: d'y dy + 4 dt + 4 = 4e "; con y(0) = 0; y'(0) = 0 %3D dt2 Determine Y (s) and the solution of the differential equation y (t).

Q: What is a particular solution to the differential equation 2y dx – 3x dy = 0 when x = 1 and y = 1?

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Q: What is the particular solution to the differential equation = (x – 1)(1 y) with the initial…

A: givendydx=(x-1)(1-y)we will solve this equation by Variable separable method

Q: Find the integrating factor of the non-exact differential equation: dy= (e2x+y-1) dx

A: Given differential equation is dy=e2x+y-1dx which can also be written as e2x+y-1dx-dy=0 Comparing…

Q: Find the general solution of the second order differential equation below: dx d) dt2 + 6x = 0 dt

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Q: Consider the spring-mass system that is modeled by the differential equation: a" + 2x' + 26x = 600…

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Q: The integrating factor for the differential equation (3xy + y)dx + (x2 + xy)dy 0 is - X Y O - Y O

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Q: Consider the autonomous first-order differential equation dy/dx = y – y° and the initial condition…

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Q: Determine an integrating factor for the given differential equation and hence general solution. (y²…

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Q: The equation y + xy2 =0, is a homogeneous non-linear differential equation True False

A: See solution below

Q: Solve the first order linear differential equation + xy = x, y(0) = –6. dx

A: A differential equation is an equation is x,y and derivatives of y. A linear differential equation…

Q: Write an equivalent first-order differential equationand initial condition for y

A: Given Data The equation is y=2-ꭍx0 (1+y(t)) sin t dt.   Differentiate the equation y=2-ꭍx0 (1+y(t))…

Q: solve the differential equation dy/dx=2x^4sqrt of y, y.0

A: Solution of given question is written in below steps.

Q: What is the particular solution to the differential equation dx 1 + y = 2e-* with y = 1, dy -1 when…

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Q: Find a suitable integrating factor to solve the first the first order linear differential equation…

A: Y(X)= x2+x

Q: Find the solution to the differential equation dz/dt=7te^(5z) that passes through the origin.

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Q: Find the Homogeneous Differential Equation of: (x2-xy+y2)dx + xydy=0

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Q: d²y dy 1 + x- -+y = x > 0 dx² dx sin(In(x))'

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Q: Find the general solution of the first-order linear differential equation (y − 1) sin x dx − dy = 0…

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Q: dy x In x = y(1+ v3+ y?), у(1) 3 1 dx

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Q: In the differential equation (xy+1)dx+x(x+4y-2)dy=0, the integrating factor is,

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Q: Consider the differential equation dx +2 +yx = 0. dt dt2 Find the general solution of this ODE and…

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Q: Calculate the particular solution for the differential equation dy dx = y+x²sin(x) with initial…

A: Given that: xdydx=y+x2sinx

Q: Calculate the solution to the differential equation dy = 2e- with y(0) = 1. dz

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Q: Write an equivalent first-order differential equationand initial condition for y

A: We have to write an equivalent first-order differential equation and initial condition for y…

Q: Find the general solution of the first-order linear differential equation. dy dx x² x > 0 y =

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Q: Find the solution of the differential equation that satisfies the given initial condition. dy y(0) =…

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Q: Convert the differential equation d²y - 3y + 2y = 4 sin x dx² dx with the initial conditions y(0) =…

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Q: Find the general solution of the first-order linear differential equation (dy/dx)+(1/x)y = 6x + 2…

A: Given- dydx+1xy=6x+2 To find- the general solution of the above first order differential equation.…

Q: Find the particular solution of the differential equation (10x + 6xsiny)dx + Vx +1(1+6y siny+10y)dy…

A: Given differential equation: with x=0, y=0. Used formulas:

Q: Solve the separable differential equation dy e*ye®* dx with initial condition y(0) = 1.

A: Given : dydx = exyeex

Q: dy Vx ev+Vx¸ x > 0 %3D X dx

A: To Find the seperable differential equation

Q: Find the solution of the differential equation that satisfies the given initial condition. dy y(0) =…

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Q: Find the solution of the differential equation that satisfies the given initial condition. dy 3XEY,…

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Q: Find the solution of the differential equation dy = cos(5x) Vy dx which satisfies the initial…

A: y'=cos5xy dydx=cos5xy dyy=cos5xdx y-12dy=cos5xdx take integration

Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: The given differential equation is dx=x9y dy. Rewrite this as y dy=dxx9.

Q: Find the general solution of the first-order linear differential equation for x > 0. dy = 30x + 14…

A: Consider the given information:

Q: (1+ex/y)dx + ex/y(1-x/y)dy = 0, a exact differential equation? If yes then, find the value of y.

A: Given differential equation is  1+exydx+exy1-xydy=0 Which is in the form of Mdx+Ndy=0. where…

Q: Solve the differential equation with the given initial value condition: dy/dx = xy + 2x ; y(0) =

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Q: Show that In y | In x dy = 0 dx +|1+ is an exact differential equation. Hence, find the solution.

A: The given differential equation is                                                         1+ln…

Q: Use Galerkin's method to formulate a linear finite element for solving the differential equation d'y…

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Q: Find the I.F of this nonexact differential equation dy/dx=1/(2xy)

A: Please see the answer below.

Q: Find the solution of the given homogeneous differential equation: xcsc ) - y dx- %3D

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Q: Find the value of n that makes the differential equation xn (3x+4y)dx +(2xn+1 +2y)dy = 0 exact.…

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Q: The integrating factor of the non-exact differential equation (x°y? + y') dx – (y° + x*y)dy = 0 is

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Q: Discretize the differential equation y" – y' + 4ty = 5(t + ), y'(-2) = 0. y'(1) = 0 with step-size h…

A: Using center difference method, we can approximate y' and y" as follows.…

Q: Find the particular solution of the differential equation that satisfies the initial condition.…

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Q: Find the general solution of the first-order linear differential equation. dy 2y dx x > 0 y =

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Q: In a spring mass system the displacement, x meters, of an object from its equilibrium position with…

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Q: Consider the autonomous first-order differential equation dy/dx = y - y and the initial condition…

A: Solve differential equation and making a equation in y0  then we fix it and we get y2 = 4e2x  then…

Q: 2(2x? + у?)dx — ху dy %3D 0

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