2x It is easy to check that for any value of c, the function Y = ce +e-* is a solution of the equation y' + 2y = e-". Find the value of c for which the solution satisfies the initial condition y(0) = 4. c =

Q: there a way to check if the equation you find after applying the initial condition is correct?

A: Let  Given that dy/dx = 2x (y − 1),.      y(0) = y0. And from solved answer The general solution is…

Q: It is easy to check that for any value of c, the function is solution of equation y(x) = ce-²ª + e¯ª…

A: The function y(x)=ce-2x+e-x. is solution of equation y'+2y=e-x Linear first order differential…

Q: Let y = Arcsec (cos² 3x). If y '= == A (B C) D) - 6 tan3x - 3 sin3x - 6 sin3x cos3x N 2 cos3x D and…

A: Note: As per our guidelines we are supposed to answer only one question if there are multiple…

Q: y' = 3x²+y² xy ; given that y(1) = 1 ; solve for y when x = 2

A: The given equation is; y'=(3x2+y2)/xy, y(1)=1.

Q: Find all complementary functions of the equation xy" - 2y'=0, x>0 1, x² x₁ x³ a. b. C. d. x, x(Inx)²…

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Q: 2xyy′ = y2 − 2x3. Find the solution that passes through the point (1, 2).

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Q: Can you elaborate how to incorporate c into the solution. Like c=0? And how does f'(0)=7 and…

A: Solution below

Q: function of xx if

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Q: In each case, find the general solution, using real-valued functions: a. y'"-2y""+y" = 0. b. y" +…

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Q: (2/x+1)(x– 1) Find the f'(x) of the function f(x) = x+3

A: Given, f(x) = 2x+1x-1x+3 f(x) = 2x32-2x12+x-1x+3 We know that ddxxn = nxn-1  and quotient rule of…

Q: Solve the IVP. (35 53 X' = X with X(0) = - (4).

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Q: Solve the equation y" + 4y = 16, y(0) = 9, y'(0) = -5.

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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.