A chemical processes a reagent whose mass, Q mg, t hours after the reaction takes place is given by Q =f (t) = 100e'. Findf (4) ,f' (4) and interpret the result.

Q: Find the general solution of the differential equation. (Use C for the constant of integration.) (ex…

A: Topic - differential Equation

Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

A: We have to find the solution

Q: Find the general solution of the differential equation and check the result by differentiation

A: Given differential equation -dydx = 2x-3             ............(1)Separating variables - dy =…

Q: Use integration to find the general solution to the differential equation: dx %3D y – 4

A: Given,         The differential equation is dydx=x-2y-4 .

Q: use appropriate substitution to solve differential equatio dy/dx-(2/x)y=-x^2y^3

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Q: When a vertical beam of light passes through a transparent medium, the reason that its intensity I…

A: We have to find What is the beam intensity at 15 feet below the surface.

Q: Solve the differential equation using variation of parameters. d’y +y= sec³(x) dx

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Q: and dr= %3D Solve for the differential of y When y=sinxx x

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Q: . Separation of Variables: x(y +1)dx+ 2 dy = 0 .

A: To find solution of differential equation using variable separable method.

Q: Use integration to find a general solution of the differential equation.

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Q: 1-dt 3- Ln(t) dt. Q10:- Calculate dx J2x t2

A: Use fundamental  theorem of calculus

Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: Use integration to find a general solution of the differential equation                  dy/dx =…

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Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

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Q: Use integration to find a general solution of the differential equation                  dy / dx =…

A: The given equation is  dy / dx = tan2 x

Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives.  A…

Q: 2. Use the method of equation Uariation of parameters to solve the differential dy - k- dx² dx xez…

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Q: What is an integrating factor of the nonexact DE  (2y^2 + 3x) dx + xydy = 0 ?

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Q: Show that cos x is the integrating factor of the linear differential equation dy/dx= sec x+y tan x

A: Integrating factors are useful for solving ordinary differential equation  that can be expressed in…

Q: The differential equation for a freee-falling mass m near the surface of the earth is given by:…

A: Consider the equation:

Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

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Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

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Q: Find the differential of the function y=xxe2x at the point x=1.

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Q: Find the differential d5y of the function y=lnx2.

A: y = lnx2 = 2lnx

Q: Find the general solution of the differential equation and check the result by differentiation.…

A: Given the differential equation:

Q: Find the differential equation corresponding to y=a cos(logx) +b sin (logx) where a and b are…

A: For a given solution having N constants , we have to differentiate the given solution for N times to…

Q: Find the general solution of the differential equation and check the result by differentiation.…

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Q: 6x2 dy dx'

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Q: Use integration to find a general solution of the differential equation                  dy /dx = x…

A: Given: dydx=x1+x2 Multiply both sides by dx dy=x1+x2dx

Q: Find dy/dx by implicit differentiation. 19) x3 + y3 = 5 20) 2xy-y2=1

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Q: Estimate the value of 217(1/3) a. approximation b. differentials

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Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

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Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

A: First Solve differential equations ,

Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

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Q: The integrating factor that transform the differential equation y" +y' + Axy = 0 into a…

A: Given - The differential equation y'' + 1xy' + λxy = 0 To find - The integrating factor that…

Q: dy :-y = xy2 dx

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Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: find the Integrating Factor and Get the General solution of the given differential equation

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Q: Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

A: First find the linear equation at x=1  then find the approximate values

Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) =

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Q: 8. Use a linear approximation or differentials to estimate the value of v15, knowing the exact value…

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Q: (2х — 5у + 3)dxх — (2х + 4у — 6)dy %3D 0 - -

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Q: What should be A for the exact differential equation of ry + A 2Ay – x -dy y? Moreover evaluate the…

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Q: 1. If f(2) = 1, find the constant of integration for dx f(x) = +3

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Q: Find the general solution of the differential equation and check the result by differentiation. (Use…

A: ∫tndt = t(n+1)/(n+1) +C ,C is a constant and for any real number n. d/dt (tn)= nt(n-1) , for any…

Q: Find the general solution of the differential equation and check the result by differentiation.…

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Q: Find the general solution to the given differential equation. (Use C for the constant of…

A: Given,         dydx=x5y

Q: Since dv = cos( x) dx, integrate the differential equation to obtain the function v. =D A dv Cos( x)…

A: Since dv=cos8xdx, the first missing term is 8. Substitute cos8xdx for dv in ∫dv to obtain ∫cos8xdx.…

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.