Let f(x) : Find the values of x where f'(x) = 3. %3D x + 4 Give exact answers (not decimal approximations). The greater solution is x = The lesser solution is x =

Q: If f '(x) = x4, what is f(x)? (Use C for the constant of integration.) f(x) =

A: We can make it easier for you.

Q: Solve the IVP d3 t3X(t) - 9x(t) = 18 e-3t dt x(0) =8 x'(0) = 9 x"(0) = 0 then find x(0.5) accurate…

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Q: Solve the differendialegimaition: (2x+e)dx + (xay co

A: Make some simplification and rearrange the given differential in exact form.

Q: The integrating factor of the given DE are already given below. What is the value of “n”…

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Q: 5. Test the exactness of ODE, if not, use an integrating factor to make exact and then find general…

A: Differential equations

Q: . The derivative of y = xe + e" is D. ex А. хе В. хе + е^ С. exе-1 + е‑

A: Given: y=xe+eπ

Q: (b) Use the method of complementary functions and particular solutions, to determine the general…

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Q: Give an example of birthrates Ai >0 such that a birth process (Xt)t>0 with birthrates di, i20…

A: The example of birthrates should follow Poisson's distribution where λi are the birthrates, since…

Q: Find f(x), the most general antiderivative of the function: f" (x) = 18x – 3 sin(x)

A: Explanation of the answer is as follows

Q: Use Newton's method to find the second approximate solution r2 to f(x) = x³ + x + 1o if x1 = 0.

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Q: y' cos x + y sin x = 2cos³x sin x- 1 What is the particular solution when y(T/4)=3v2 ?

A: Given differential equation is y'cosx+ysinx=2cos3xsinx-1 we have to find the particular solution…

Q: If an initial condition is given, find the corresponding particular solution. Throughout, primes…

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Q: a) A capacitor (C) which is connected with a resistor (R) is being charged by supplying the constant…

A: Given : E = ∫0∞P(t) dt  ,   P(t) = 5Re-tRC2×R

Q: Determine weather the statement is true of false. Explain your answer.

A: Given: ∫cos x dx = sin x+ c∫cos x dx = (sin x + π) + C To find: Whether the  statement true or false…

Q: The derivative of the function y = (3e* – x²)(cos x) is: a) y' = (3e* – 2x) cos x – (3e* – x²) sin x…

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Q: For a given function ƒ, explain the steps used to solve the initialvalue problem F '(t) = ƒ(t), F(0)…

A: Consider the following differential equation: F't=ftdFtdt=ftdFt=ftdt Integrate the above equation:…

Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

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Q: Solve f(x) Sin e* (4 nodes) Using Gaussian Integration (Numerical Methods) [ f(x) dx

A: Given function is f(x)=sinex We have to calculate ∫-11sin(ex)dx Formula for 4-point gauss quadrature…

Q: 51. The functions y = e* and y = x³e do not have elementary anti- derivatives, but y = (1 + 3x)e"…

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Q: Solve the initial value problem to find f(x), given 2 =1+ 4x? when f(-1) = 4 dx

A: Satisfied condition of differential equation

Q: (1) (a) Find the derivatives of functions f(x) = e2 and g(x) = 5æ?. (b) Compute the definite…

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Q: dx 1. dt xt x(0) = 1, solve for x(0.3) when h = 0.1 I| -

A: Given function is, dxdt=-12xt,   x(0)=1, h=0.1 and we need to solve, x(0.3)   Here we have, (t0,…

Q: The integrating factor of the given DE are already given below. What is the value of "n" y(y²-x-6)dx…

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Q: dy Solve the initial-value problem for y as a function of x. (49 – x²). dx = 1, y(0) = 4 Y =

A: We will solve this integration using trigonometric substitution as follows

Q: Find the total derivative dy dw. Y=3x+2w+5z x=4 In(w*) z=e43x³

A: Given, y=3x+2w+5z2x=4ln(w2)z=e-z+3x-3

Q: The integrating factor of the given DE are already given below. What is the value of "n" yly²-x-7)dx…

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Q: Some elementary functions, such as f(x) = sin(x2 ), do not have antiderivatives that are elementary…

A: let ∫x-necxdx for n a positive integer and c a non zero constant is non elementary since…

Q: Find the linear use it to estimate ln(1.44). L(x) = In(1.44) approximation of f(x) = In x at x = 1…

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Q: π/2 g(x) = 2x + 4 sin² x g(t) dt. - n 0

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Q: Solve the initial-value problem. dy for x20 with y(0) = 2 5 dx The solution to the initial-value…

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Q: the integrating factor of the FOLDE y'-2xy=x is e^-x^2, show your solution

A: Recall: Linear differential equation of first order :    dydx+P(x)y =Q(x)…

Q: 44. Solve for the second derivative of y = e5x а. 25е5x b. 25e4* c. 25e3* d. 25e2x 45. Find dy/dx of…

A: NOTE: Refresh your page if you can't see any equations. . take derivative take the second…

Q: Find f(x) by solving the initial-value problem. f '(x) = 8ex − 4x; f(0) = 12

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Q: For what function P is the integrating factor α(x) equal to x?

A: We know that , integrating factor of the differential equation is

Q: If f'(x) = 4x°, what is f(x)? (Use C for the constant of integration.) f(x) = %3D

A: It is known that ∫xn dx=xn+1n+1+C provided n≠-1. Given that f'x=4x3. Integrate as follows.

Q: find the general solution of dy/dx + (3/x)y=2/x^2 as a function of x

A: Given,           dydx+3xy=2x2

Q: Find a positive constant that satisfies the equation: ∫(1/x²+a²)dx=1    integration limits: [ 0,…

A: Consider the equation ∫0∞1x2+a2dx=1 We have to find the value of a Use integral formula…

Q: If f'(x) = 5x*, what is f(x)? (Use C for the constant of integration.) f(x) =

A: To find the integration

Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: * The solution of | x + 3| = 4 is :18 7 or 1 O 1 or -7 O 7 O the integration of the function below…

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Q: Q1: Find the Integration using Gamma Function Method: x*e-3xdx 0.

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Q: Find Solution of the Attached ?

A: Given differential equation is 3xy'-y=lnx+1 and y1=-2. Given differential equation can be written in…

Q: Solve the initial value problem by using integration. g' (x) = , 9 (1) = 4 x+1 %3D

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Q: 3. Show that the DE is not exact, determine the integrating factor, make it exact and solve. a. (2y…

A: The given differential equation is…

Q: The integrating factor of the given DE are already given below. What is the value of "n" yly²-x-8)dx…

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Q: -8 dx c – 2)(x² + 4) an upper-case "C" for the constant of integration.

A: We use partial fraction to find integral

Q: 16 Suppose we know that (3fx)-2)dr-6 4 and that Sxf (x²) dx =8. ise this information and properties…

A: We have to find ∫04fxdx

Q: Consider an animal population P(t) with constant death rate 8 = 0.01 (deaths per animal per month)…

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Q: Solve the following initial value problem for  y = f (x). dy dx  =  e−3x, y = 79  when  x =…

A: dydx=e-3x and y=79 whrn x=0

Q: Find the general antiderivative of the function f(x) = +3 sin x - : 1 1+x?

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