51. The functions y = e* and y = x³e do not have elementary anti- derivatives, but y = (1 + 3x)e" does. Evaluate |a + 3x*)e*dx.

Q: findthe differential dy of the given function. y= arctan(x − 2)

A: we have to find the differential dy of the given function. y= arctan(x − 2)

Q: Answer the following using Homogenous ODE in Differential Equation. [x csc( c() - y] dx + xdy = 0

A: we have to solve the following homogeneous ode

Q: E. Solve tne differential Equotions ☺ Czxy + xln3x)dy + .(xtyJ dx =0 when x =3, y=2

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Q: If z = +3y, find the differential dz. dz =

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Q: Find the differential dy of the given function.

A: Here we will Compute the first derivative dydx  And the rule we will use for computing is known as…

Q: 04- Determine the general solution of the following differential equat dy tan x. +у %3D sec х dx

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Q: Ho Find (dy/dx) for: tanh-¹(x y) + e(x+y) 5 cos(y)

A: It is given that, tanh-1xy+ex+y=5cosy. The objective is to find dydx. Formulas used:…

Q: 6. Write down the differential, dy, of y = e3x.

A: to find the differential of y=e3x

Q: Solve the following differential eyuation x 2+ 2y = x* e** y.

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Q: I. Find dy/dx of the following: 1. y= In 2x 2. y (In x) 3. y= In(tan x)

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 5.32. z = sin(x² + y?)

A: To find the differentials of third order.

Q: Q: If In/x² + y2 =sec(), use implicit differential to proof the following dy _ -x(x²+y²). sec. tan?…

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Q: Answer the following using Homogenous ODE in Differential Equation. 3xydx + (x² + y²)dy = 0

A: Hint: By putting y=vx we can solve homogeneous differential equation.

Q: 2. Z dx dy dz to

A: (5) Given integral is ∫02∫04−z2∫02−zzdxdydz.…

Q: Find the differential dy of the given function. y = 3x − sin2x

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Q: Prove that the function y = ecos* satisfies the differential equation: y" + sin(x) y' +y cosx = 0

A: Find y' , y" and put into given differentiatial equation.

Q: consider the differential equation dy/dx=sin(x)/y for which the solution is y=f(x). Let f(0) = 1…

A: Given dydx=sinxy, y0=1. By variables separation,  y dy=sinx dx Integrating on both sides,

Q: Find dy/dx at the given point without first solving for y. x2 + 4xy + 23 = 0 at (1, −6)

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = - cos( 7x - 1 dy =

A: We have to find dy for the given function y=17cos7πx-12.

Q: The non-exact differential...(x² + y²)dx + (3xy2 + 2xy + x³)dy = 0 can be reduced to exact after…

A: We need to determine the integrating factor for the differential equation: x2+y2dx+3xy2+2xy+x3dy=0…

Q: Q:: If In /x2 + y? =sec(), use implicit differential to proof the following: - dy -x-(x2+y²). sec.…

A: Please see the explanation below..

Q: Find dy/dx for y = 3l(sin-(e-3**)12 dy 3(sin"(e-*)* In3 2(sin-"(e-3x*)- dx 1(-6х) V1-e-6x2

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Q: Find the differential dy of y = tan x for x = π/4 and dx = −0.1.

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Q: I. Find dy/dx of the following: 1. y= In 2x 2. y= (In.x) 3. y = In(tan.x)

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Q: The differential equation (3ycosx+ 4.xe* +2x'e" dx+ 3(sin x+1)dy 0 is exact because OM ON Ox

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Q: 1. Suppose that y = x³ + 4x. Suppose we increase x from 3 to 3.02. Use differentials to estimate the…

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Q: 5. With the substitution cosy == differential equations sin y dy – cosy(1 – x cosy)dx=0 reduced to a…

A: Substitute  cosy=1tNow differentiate it with respect to t,-sinydy=-1t2dtsinydy=1t2dt

Q: Let e 2* = 2 find dy dx at x = 1

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Q: the differential equation (e* sin(y) – 2ysin(x))dy + (e* cos(y) + 2cos(x) is exact Select one: O…

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Q: 24. What does it mean to say that dV is an exact differential?

A: What do you mean by dV is an exact differential.

Q: (a) Find thne derivative. y = In(4x – 6) – 3 In(x) dy dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: 22. Find OY if y2 - 4xy + x² = 10. dx

A:

Q: 3) Find dy given 3xy = In x. dx

A: Given  3xy=lnx To find dydx   implicit differentiation is used Both sides have to be differentiated…

Q: Let y=(x to the 2nd power +3) to the 2nd power . Find the differential dy when x=4 and dx=0.2…

A: Given,    y=(x2+3)2

Q: Solve the following differential equation given the initial value. dy = tan(x), y(0) =1 dx A y = In|…

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Q: The appropriate integrating factor for the following differential equation (3xy – y?)dx + x(x - y)dy…

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Q: dy + ytanx = y° sec° x dx

A: We have to solve given problem:

Q: 1 Solve for the differential of y when y=sinzx, x=÷, and dx= - 3 A) B) 2 -- C) D)

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Q: Find the function y: (0.x) → R that satisfies the ordinary differential equation ry'(x) + y(x) = x²…

A: Given : y : 0 , ∞→ℝ   ;  xy'(x)+y(x)=x2 cosx        ;  yπ = 0 To Find : solution of ordinary…

Q: Q:: If In/x2 + y² =sec(), use implicit differential to proof the following: - -x-(r+y?). sec. tan…

A:

Q: 1. Given y = 4e* + In x, find the differential dy.

A: See the attachment

Q: Consider the following differential equation. (x2 + y2)y′ = y2 Let  f(x, y) =  y2/x2 + y2 .  Find…

A: This is a problem of differentiation of the function. Based on the general formula we will answer…

Q: 5. y = e-cos(x) dy dx

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Q: The differential equation (3ycosx+ 4xe* + 2x²e* ]dx + 3(sin x + 1 )dy = 0 is exact because ƏM ƏN

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Q: If y = In(6 + x8), find the differential dy. Your answer will be in terms of x and dx. Enter dx as…

A: topic - differentials

Q: Find the value of the differential dy for y = e3x + 5x if x = 0 and dx = 0.1.

A: We know the differential dy of  y=f(x) is given by, dy=f'(x) dx

Q: - if eV = In(x) + In(y) + e³ ху 3 Find dx

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Q: Approximate Ay using differentials for y = x2 - 4x at x = 6 when Ax dx = 0.03.

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Q: What is the general solution to the differential equation (tan x)dy – (4y In y – y tan³x)sec²x dx =…

A: We will convert given differential equation into linear differential equation by appropriate…