Find the value of C so that the function y = e * (x + C) is a solution to the differential equation dy y = e-a with initial condition y(-2) = e2. dx

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Q: Determine whether the function y = 3 cos 2x is a solution of the differential equation y(4) − 16y =…

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Q: 1. Given the function f (x) xe +e*, verify it is a solution to the differential equation y" + 2y'+y…

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Q: Let y be a solution of the differential equation V = +3, where x > 0, y > 0 2ay such that y(2) = 6 .…

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Q: dy = xe with y(0) = 4 dx

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Q: 2. Solve the differential equation dx for y = f(x) with the initial condition y(0) = 2.

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Q: The general solution of the differential equation using exact or non – exact dy/dx + y/x = 1 is, O…

A: Given that :dy/dx +y/x = 1  Find the general solution of this differential equations. Here i…

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A: Find the second derivative and substitute in the given differential equation and solve for r.

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Q: し y(x) ¥(0)%=3

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Q: Find the solution of the differential equation that satisfies the given initial condition. y/ tan…

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Q: Verify that the function y = e-3x is a solution to the differential equation d2ydx2 + dydx − 6y = 0.

A: We have to verify the solution

Q: Let y, = cos() be a solution to t y" -y' +q(t) y=0. Find a second linearly independent solution to…

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Q: determine the value of C of the general solution of the separable differential equation dy/dx= 2y/x…

A: Given: A differential equation dydx=2yx As this is a separable differential equation so it can be…

Q: Find the particular/primitive solution to the differential equation (y+y cos x - yex)dx+2(x5+ln x -…

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

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Q: y' = 5y + e-2*y-2

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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: Find the solution of the differential equation that satisfies the given initial condition. y/ tan…

A: Given differential equation Initial condition

Q: From the differential equation dy = x2 dx, what is the equation of y in terms of x as the curve…

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Q: Find a second solution of each differential equation. x²y" + xy' + y = 0; y1 = cos (In x). (1+x)y" +…

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Q: Verify that the function y (x) = ln (x + c) is a solution of the differential equation e^y y` = 1…

A: The given differential equation is: ey y'=1

Q: dy 2 dx y+2 x+y- 1

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Q: By using the substitution z = y², convert the differential equation dy x²y- xy2 = 1. dx to a linear…

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Q: Find the solution of the differential equation (In(y))³ dy dx = x'y 3 which satisfies the initial…

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Q: Determine whether the function y = ln x + e2x + Cx4 is a solution of the differential equation y(4)…

A: Given differential equation is y(4)-16y=0 Given function is y=lnx+e2x+cx4 Differentiate y repeatedly…

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

A: Given : dydx = exyeex

Q: determine the value of C of the general solution of the separable differential equation dy/dx= xy^2…

A: From the given problem: dydx=xy2 So, dydx=xy2dy=xy2dxdyy2=xdx Now integrate on both side:…

Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: Given differential equation is:  d2ydx2-2dydx+y=e-4x(x-1);     y'(0)=0, y(0)=0 Solution of…

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A: To find the particular solution of differential equation xdy=x+y+2dx    x>0y1=10

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: What is the particular solution to the differential equation dy/dx=(x-3)y with the initial condition…

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

Q: 1.) Obtain the general solution of the differential equation dx – (1 + 2x tany) dy = 0.

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Q: Find the general solution of the differential equation. (Use C for any needed constant.) dy = 5 - y…

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Q: Find the particular solution to the differential equation dy/dt = e^(t+y) that passes through (1,0),…

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Q: Solve for the particular solution of the differential equation 2xy = x² + y² with the given…

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Q: Find the indicated particular solution of the differential equation. dy dx + 7y= -2e - ⁹x; x = 0…

A: Topic = Differential equation

Q: Find the solution of the differential equation that satisfies the given initial condition. x +…

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Q: Find the particular solution of the given differential equation of order one below, such that when x…

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

A: Given:        dydx= 14+x2…

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Q: determine the general solution to the given differential equation on (0,∞). Q. x2y′′+3xy′+y =0

A: Differential equation: x2y''+3xy'+y=0Now we put a substitutionz=log…

Q: Let F(x) be the particular solution of the e2x differential equation Y"-2y +y = (e* + 1)? * What is…

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

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Q: dx x2-y2-xy 0 ху dy

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Q: | Find the solution of the differential equation (In(y))³ dy = x'y dx which satisfies the initial…

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