EXAMPLE 1 A separable equation Find a function that satisfies the following initial value problem. y'(t) = y'e, y(0) = }

Q: (1) The functions f, g and h are related by f(x) = g(x+1),. g'(x) = h(x-1), then f"(2x) equals: (a)…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: = 8x - 3y2 nd the Implicit derivative " dy/dx" of the function. A) y' = - 6y B y' = 8 - 6y (Cy' -6y…

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Q: (2) (a) Let g(x) be a function with g'(1) = 8. Using differentials estimate the value of g(1.2) –…

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Q: x(1-x2)2y'' - (1-x2)2y' + x3y = 0  Cauchy - Euler differential equation your solution.

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Q: Example 4: Solve iv) y" – 2y' + y = 3e2x.

A: Given differential equation is, y"-2y'+y=3e2x The auxiliary equation of this differential equation…

Q: (1 point) Solve the initial value problem yy' + x = Vx² x² +y with y(1) = -V3. a. To solve this, we…

A: We solve the remaining part of the question by separating the variables.

Q: y (sec(ln x)' ху" + у' +-%-

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Q: (a) Let f(x) = 2e²+² + e8. ƒ'(0) = (b) Suppose that f(x) f(x) = 3e² ƒ'(3). ƒ'(3) = - exe. Find

A: Part a Givenf(x)=2ex+2+e8 We are required to findf'(0)   Part b Givenf(x)=3ex-exe We are required to…

Q: x(1-x2)2 y'' - (1-x2)2 y' + x3y = 0  cauchy - euler differential equation find the solution.

A: Given differential equation is                   x(1-x2)2y''-(1-x2)2y'+x3y=0 The differential…

Q: Which one of these equations is not separable? (1) xy' = y ln |x| (2) y' = In y' (3) = x + sin(x)…

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Q: -pf'(p) Let q = f(p) be the demand function for a certain commodity, where q is the demand quantity…

A: Given q=f(p)E(p)=4p+1E(p)=-pf'(p)f(p)

Q: e'y' = e + 4x, y(1) = 5. %3D y =

A: First we convert the given differential equation into an exact differential equation by multiplying…

Q: Please show step by step

A: These are our equilibrium solutions. Now, we analyze the sign of the derivative around these…

Q: Solve x' = y – x +t y = y x(0) = 6 y(0) = 8 x(t) = help (formulas) y(t) = help (formulas)

A: The solution is given as

Q: Find the solution to the differential equation that satisfies the given condition. I am having…

A: Given differential equation can be written as Integrating both sides , we get

Q: A polluted pool has an initial concentration of bacteria of 10* part/m2, while the a) acceptable…

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Q: A tank contains 1900 L of pure water. A solution that contains 0.01 kg of sugar per liter enters the…

A: Given that a tank contains 1900 L of pure water. A solution that contains 0.01 kg of sugar per liter…

Q: Solve the differential equations: (a) = 4x+2x+5 where V(1) = 10 .

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: y" - y' - 2y= e* %3D

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Q: f (x) = 1+e4x

A: Note: As per our guidelines, we are supposed to answer only one question. Kindly repost the other…

Q: Evaluate the given differential equation (1+ cosx)y' = sinx(sinx + sinxcosx - y) a.y = x - sinx + C…

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Q: (1 point) Find the solution of the differential equation xy' + y = y² that satisfies the initial…

A: The differential equation is with the initial condition .To Find:The solution of the differential…

Q: Solve xy' = y +1

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Q: The equation of the tangent line to f(r) = at z = 1 is y = ar +b and the tangent point is (1, c).

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Q: Equation in (a) becomes the non-homogenous equation, y'' − 2y' +y = e^2x . Solve the particular…

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Q: Rapid technological advancements have many many products obsolete. The rate of change of the market…

A: We are given that the rate of change of the market share of a new product (z) will be proportional…

Q: Bernoulli's Equation Solve (dy/dx) - (y/x) = y2e^(x2

A: Since you have asked multiple question, we will solve the first question for you. If you want any…