y = y2- 4y + 4

Q: Find the differential equation whose solutions correspond to the following equation 1. y = C,e¬* +…

A: Apologies. We only answer one question at a time. We will answer question 1 as the exact one wasn't…

Q: Find a ge neral solution to the differential equation. y" - sy'-a4y = 0

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Q: Find a general solution to the differential equation. y' + 2y = 2 tan 2t - 3t 21-11e³1

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Q: Find the value of b, if a = 6, so that the general solution of this ordinary differential equation…

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Q: Find a general solution for the given differential equation with x as the independent variable.…

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Q: Determine whether the function y = 2 sin 2x is a solution of the differential equation y"-8y = 0.

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Q: Find a particular solution to the differential equation using the Method of Undetermined…

A: Given that Find a particular solution to the differential equation using the Method of Undetermined…

Q: G(m1+m2) 1) +y de h2 This is an oscillating differential equation. So the answer to this equation…

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Q: Determine whether or not y=C1 cos (2t) + C2 sin (2t) is the solution to the differential equation…

A: we check y=c1 cos(2t)+c2sin92t) is the solution to the differential equation y''+4y=0

Q: dy 3(1 + P) - 2ty(y³ – 1) dt

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Q: d. 2ydx +x(x² In y – 1)dy = 0 -

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Q: Find the general solution of the differential equation: y' + 2y = xy?. Use lower case c for the…

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Q: b. 6y²dx – x(2x³ + y)dy = 0 -

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Q: Solve the differential equation, subject to the given initial condition. dy + 4y = 5x²; y(2) = 21 y…

A: we need to solve the given initial value differentialequationxdydx+4y=5x2  ; y(2)=21The solution is…

Q: a) Solve the following first-order differential equations: dy = -y 2x, given that when y=0, x=+2 dx

A: We have given  -y dy/dx = 2x when y = 0 and x = +-2

Q: Find the general solution for the differential equation: 1- y" - 4y = 1+ 65e'cos(2t)

A: Given : y'' - 4y = 1+65et cos(2t)  To find : General solution of the given DE

Q: Find the solution to the differential equation below such that y(0) = 8 y' = 8xy – 2x y(æ) =

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Q: find the general solution of the given differential equation. 4.y″ − 2y′ − 3y = −3te−t

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Q: The auxiliary roots for the differential equation y"" - y = x^2 are equal to 1. a. FALSE O b. TRUE

A: Follow next step

Q: Find the particular solutions for the following differential equation: y`+2xe^-X^2=0, y(0)=4

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Q: Show that the following first order differential equation is exact, and then find the general…

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Q: 13. y" - y'- 12y = 0; y = Ae** + Be-3*

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Q: Show that if the roots of the auxiliary equation of a differential equation are r = p± qi, then the…

A: The given roots are r=p±qi. Show that the differential equation itself is y''-2py'+p2+q2y=0. Here we…

Q: Find the general solution of the differential equation given below ylnxlnydx + dy = 0

A: We will solve it using separating the variables

Q: Find the general solution of the differential equation (D² – 6D + 8)y= 6² + cos 6x

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Q: Find the general solution of the following differential equation. 1 y" +y 1 y = In r

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Q: Find the two values of K for which y(x) = ekx is a solution to the differential equation yII -…

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Q: find the general solution of the given differential equation. 6.y″ + 2y′ + y = 2e−t

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Q: Find a general solution for the given differential equation with x as the independent variable. y(4)…

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Q: (5y – 6x)dx + rdy = 0

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Q: Solve the differential equation using [y(0)=1} to find C 2æydx + (x² + 3y) dy =

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Q: Find the general solution of the given differential equation: 3t?y" + 7ty' + 10y = 0 %3D

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Q: find the general solution of the given differential equation. 5.y″ + 2y′ = 3 + 4 sin(2t)

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Q: Determine the general solution to thegiven differential equation. (D + 1)(D − 5)y = 0.

A: Given:D+1D-5y=0

Q: dy dx 6e²x-y

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Q: Show that the following first order differential equation (xe" + 2ye")dy + (yxe" + ye" + y²e") dx =…

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Q: Solve the given differential equation by undermiNed coeFFicients. 1. y" +6y +9y = -xe 4x

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Q: Find the particular solution of the differential equation: y' + 9y = 7 sin³t+ 2te* – t² %3D

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Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: Find a particular solution to the differential equation y + ly – 12y = –288t.

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Q: Find the general solution to the differential equation y" + 49y = cos (2x). %3D

A: Consider the given differential equation y''+49y=cos2x. The characteristic equation is m2+49=0. That…

Q: (d) Find an appropriate integrating factor for this differential equation and solve it downright, y'…

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Q: Find the general solution of the given differential equation, and use it to determine how solutions…

A: Consider a first order linear differential equation of the form . This differential equation can be…

Q: Find the particular solution of the differential equation: / + 9y 7 sin t+ 2te-t

A: We have to find the particular solution for the differential equation…

Q: Find a general solution to the given differential equation. y" + 9y 0

A: We are given homogeneous second order linear differential equation with constant coefficient we need…

Q: Show that the following first order differential equation (xe + 2ye") dy + (yxe + ye" + y²e*) dx = 0…

A: Given that: (xex+2yex)dy+(yxex+yex+y2ex)dx=0

Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: State the order of the differential equation and verify that the given function is a solution. (1 -…

A: It is given that, 1-t2y''-2ty'+2y=0, yt=t. Now, Differentiate yt=t as follows: y'=1 and y=0.

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.