y" + 2y' = sin 2x ||

Q: find the integrating factor of cos(x)y'+sin (x)y=2cos^3(x)sin(x)-1

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Q: Find the linearization of ƒ(x) = √(x + 1) + sin x at x = 0. How is it related to the individual…

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Q: The linear approximation at x 0 to sin(2x) is A + Bx

A:

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

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Q: Solve for the differential of y when y = sinæx, x=-, and dx=- 3 2 4 4 -iN

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Q: Use integration by parts to verify the reduction formula.

A:

Q: Solve for the differential of y when y=sinzx, x=-, and dx=- 3 2

A: Pi/4

Q: Verify the integration formulas ∫sech x dx = sin-1 (tanh x) + C

A: To verify: The integration formula, Formula used:

Q: Find the differential of z = sin²(5x) + ev

A:

Q: dx S COsxtanx

A: Here we will solve the given integration,

Q: Only I method. Except Exact DE (x+2y-1)dx+(2x+4y-3)dy oo

A: First we campare the given differential equation Mdx+Ndy= 0 and then solve it.

Q: In x 2. Integrate -dx , (i) using the sub stitution u = Inx (ii) using integration by parts.

A: Integrate by substitutions and by parts

Q: (solve exact de) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xye )dy

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Q: What is the integrating factor of (y – cos² x) dx + cos xdy = 0?

A:

Q: Q2 Integrate by parts: ex sin x dx

A: find ∫exsinxdx we know, ∫u.vdx=u∫vdx-∫dudx∫vdx now, apply this on equation I=∫exsinxdx…

Q: Find the particular solution for the given separable equation when y(0) = 3. 1 dy = ysin(2x) 1? dx

A: To find the particular solution for the given separable equation when y(0)=3

Q: dy cosx+ ysin x =1 dx

A:

Q: Compute the differential dy  for  y=(6x+sinx)^3

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Q: Explain why the linear approximation to ƒ(x) = cos x at x = 0 is L(x) = 1.

A: The linear approximation, or tangent line approximation, of f at x=a is defined as Lx=fa+f'ax-a This…

Q: The position of a particle moving along the x-axis is x(t)  = sin(2t) - cos(3t) for time t>= 0. When…

A: Given the position function, x(t)=sin2t-cos3t

Q: Solve for the differential of y when y=sinxx• x=-. and dx= 3 4 2

A: i am going to solve the given problem by using some simple calculus to get the required result.

Q: Solve for the differential of y when y= sinzx. x= -, and dx 3 2 4

A: we have to solve the problem

Q: Compute the differential dz of the function. 3,,10 x°Y %3| dz

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Q: Find the general solution for (cosx)y' = 1 – y² consider y, (x) = sinx. %3D

A: Given:  cosxy'=1-y2                  1          , y1x=sinx Let y=y1+u be a solution of (1)…

Q: 23, zax + sec(x)cos(y) 0, y(0) = 0

A:

Q: (3+y +2y² sin2x) dx + ex + 2xy -y rin 2x) dy=O

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Q: Find a result by using homogenous for (x³ - 3x²y)dx-(x3³ - y³)dy = 0

A: This question is based on solution of Homogeneous differential equation.

Q: 5 dy of: y = |x sin 2 + tan (x") dx 4

A: Given function is y=xsin2x+tan4x75 We have to find dydx. Here, we have to use some rule of…

Q: (a) Determine f 2xe3*dx by using integration by parts. (b) Determine S cos(x²) 2x dx by using…

A: Given,  ∫2xe3xdx ; We have to integrate using integration by parts ∫cosx22xdx ; We have to…

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your v?

A: Solution

Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

A:

Q: In integrating the function fx cos(3x) dx using integration by parts, what would you choose for your…

A: Let ,I=∫ xcos3xdxSubstitute  u=3xdifferentiate du=3dx⇒du3=dxI=∫ u3cosudu3I=∫ucosu9duTake the…

Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

A:

Q: y= sinh-lx then prove that Vx2+1 dx

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Q: find the differential dy if y= sqrt(2x^5-3x

A: Given query is to find the differential of the expression.

Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…

Q: 2. Use integration by parts to solve for [x³c x³ cosx dx.

A:

Q: Solve for the differential of y when y=sinxx: x=-, and dx 3 2 2 2 4

A: y=sinπx, x=13, dx=12

Q: Find the differential dy when x = 3 and dx = 0.2 %3D

A: When you get function of function form to differentiate, we use the chain rule. y = f(g(x)) dy/dx =…

Q: Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual…

A: To determine the linearization of the function at x=0.

Q: tion to (1+ x²) dy + 2xy = 4 that satisfies the initial condition y(0) = 0. dx %3D %3D

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Q: Find dy/dx by implicit differentiation   4Sin (x2) =x Sin (y2)

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Q: Integrate by parts f(x)=sin4(x)cos3 (x) dx

A: Given the integral  I = ∫cos3(x) sin4(x) dx cos2(x)=1−sin2(x) I = =∫cos(x)(−sin4(x)(sin2(x)−1)) dx…

Q: f(x csc² 2x - x cos 2x)dx

A: The given integral is ∫xcsc22x-xcos2xdx. The objective is to solve the given integral. Following…

Q: 2. f x cos² x dx

A:

Q: b) By using integration parts, show that ii. S(3x + 5) sin(2x + 3)dx = -÷(3x + 5) cos(2x +3) +sin(2x…

A: By using integration by parts, show that∫3x+5 sin2x+3 dx=-123x+5 cos2x+3+34 sin2x+3+C

Q: Test for homogeneity

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Q: B4. Evaluate e* sin x dx by using integration by parts method.

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Q: integral from 0 to pie over 4 of sin^2 (4x) cos^2 (2x) dx

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Q: 1. Use integration by parts to find (3x – 1) sin x dx.

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