y" (t) + ky' (t) + y(t) = 8(t – 1), y(0) = 0, y'(0) = 0 %3D

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Q: i. Determine the general solution of the above differential equation.

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Q: Find a first order differential equation for which y2 sin(xy) + (2xe)cos(x)) = 3 is an implicit…

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Q: use the method of variation of parameters to find a particular solution of the given differential…

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Q: • / = Ity

A: y'=x-yx+y It is a homogeneous differential equation. Put, y=vx⇒y'=v+x·dvdx Therefore,…

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Q: Form a differential equation from the given function. y = Asin(2x)-5cos(2x)

A: Giveny=Asin(2x)-5cos(2x)   ----{1}

Q: 2. Form the differential equation from the circle passing through the origin having their centers on…

A: This question is based on forming differential equation by eliminating constant.

Q: A heart pacemaker consists of a switch, a battery of constant voltage Eo, a capacitor with constant…

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Q: Determine the solution for the differential equation ry = In(x) for which Y(1)

A: y^2 = (ln x)^2  + 2 ln C

Q: Find a particular solution yp of the nonhomogenous differential equation y(3) + y' = x sinx + x²e* +…

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Q: The linear Differential equation of any order if there is no constant term s present is known as?

A: We have given The linear Differential equation of any order if there is no constant term s present,…

Q: Form a differential equation by eliminating arbitrary constants "A" and "B" from the family of…

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Q: By using suitable method, form an ordinary differential equation by eliminating constant A from the…

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Q: y' - y = 2x? 3

A: Given:   y' - 3xy = 2 x2   To Find: An explicit solution of the above differential equation by…

Q: What is the particular solution to the differential equation +1+y = 2e- with y = 1, 2=-1 when x = 0?…

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Q: Use separation of variables to find the general solution of the differential equation. 6 cos(tx) xp

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Q: The independent variable x is missing in the given differential equation. Proceed as in Example 2…

A: Given:y+8yιι =yι2   →1Let yι =u →Ad2ydx2=dydxd2ydx2=dudy=dydxd2ydx2= ududy →Busing Aand B in 1we…

Q: Consider the solution to the differential equation y' with y(1) = 1. 3x (a) Apply Euler's method…

A: Given y'=4y3x with y1=1 Here, x0=1, y0=1 (a) We will find the value of y2 by Euler's method with a…

Q: the given differential equation is not exact and hence show that Solve it x²ydx -lx3+y?)dy=0

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Q: Find the general solution for the second-order differential equation ¨y + 8 ˙y − 9y = −3 with…

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Q: Find the differential equation of the family of cissoids: y^2 = x^3/ (a-x)

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Q: Determine the appropriate form for yp on the differential equation y" = 9x^2 + 2x - 1 %3D

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Q: y" + 9y = 9sec²3x %3D

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Q: Eliminate the arbitrary constants in the equation defined by y = ae^(3x) + bxe^(3x). Which of the…

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Q: y(4) – 16y" = e¯* + sin3x y

A: find complementary function and particular integral and add them

Q: 2.Form the differential equation from the family of curves y² = Ae³* + Be* , where A and B are…

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Q: Use the method of Undetermined Coefficients to find a PARTICULAR SOLUTION to the differential…

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Q: Show that the differential equation dy -2 - yezy dr rezy – 2y is exact and find its solution. 3.

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Q: If we use the method of variation of parameters, the particular solution of the following…

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Q: Consider the Non-Homogenous differential equation: y"-y= 6sinx Given that y. = Ce* + Cze-*, using…

A: Suppose we have second order linear differential equation as .  Consider are independent solutions…

Q: use the method of variation of parameters to find a particular solution of the given differential…

A: solution:-  The given differential equation is  y''+4y=cos3x The auxiliary equation of above…

Q: use the method of variation of parameters to find a particular solution of the given differential…

A: To solve the following differential equation using the method of variation of parameters to find the…

Q: Write down a linear homogenous differential equation (with the smallest order and constant…

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Q: This is a differential equations problem.

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Q: Find the general solution of the first-order differential equation                       y cos x −…

A: Given: y-1cosx+dydx=0 for finding solution of given differential equation, we use variable separable…

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Q: Obtain the general solution of the given Differential Equation using the Method of Variation of…

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Q: y = ry' – In (y')

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Q: is there any homogeneous linear second order differential equation such that two functions e* and t²…

A: Given: The two functions and   is the solution of the second order differential equation

Q: A heart pacemaker consists of a switch, a battery of constant voltage Eo, a capacitor with constant…

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Q: 3. Find the particular solution to the differential equation (y + 5)(x+2) if the %3D dx solution…

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Q: y' = ycotx + y²cscx

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Q: a. y = Ae-3x + Be2* . Derive the differential equation by eliminating the constants

A: here we have to go differentiating and substituting

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A: To find the particular solution for the given differential equation which satisfies the initial…

Q: Find the differential. Equation by eliminating the arbitrary constant  y = Ae2x + Be-2x

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Q: use the method of variation of parameters to determine the general solution of the given…

A: First calculate the complementary function.