Order One DE xy'-2y=x3cos4x

Q: Separate tanh-1(x+ iy) into real and imaginary parts.

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Q: xe 2, x Cosz dx

A: Integration by parts, ∫udv=uv-∫vdu u is the first function Given integral, ∫x exdx

Q: Find dy Y= 5In CI+x") 4 dy'=?

A: The solution are next step..

Q: 2x cos(2x)dx

A: Given : ∫2xcos2xdx

Q: fino plYZ11?

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Q: Differentiate. y = Jex +8 dy dx

A: The given equation is y=ex+8 To find: dydx

Q: dy ion =1+y de uden Teul

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Q: 76. Use integration by parts to obtain the formula VT=* dx = +VT=x + 1 dx. 1 – x?

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Q: 23 dx V25 – x2

A: We integrate the function using trigonometry substitution.

Q: Find the total differential. z = 5x3y9 dz =

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Q: y = sech /2 + v2x + 1 + tanh v8x² + 3

A: To find the derivative of the function

Q: Suppose that 2 J of work is needed to stretch a spring fromits natural length of 30 cm to a length…

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Q: 1. S(3 – 2x – x*) dx

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Q: dx + 3tx = t4 Int+1, dt 2. t2. %3D

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Q: Find two z values so that 48% of the four decimal places, separated by a 0,0.

A: Given Data: Z is the standard normal distribution   P(-x<z<x)=0.48 P(z<x)=0.74

Q: Finel for r=1-Sino

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Q: Simplify (if necessary) then Compute: y" +y' for [6(cosh2x- sinh2x)] d -3x2 dx a2 y(z) = [; (z²x+…

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Q: sech? dx 1- sech Vĩ tanh Vi dt Vi 2-

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Q: sketch, eva luate freverse integ ration order of 2. 2. 4-X 2y e dy dx 4

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Q: y = sinx from x = = to x = n and the x axis 2

A: The required solution is:

Q: is 4= Sinh(2sinhix) shaw Hh at %3D 2 (a)

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Q: 9. Differentiate y = /sec³ (5t2)

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Q: Y2-1 dy

A: Follow the procedure given below.

Q: 3 tanh (In(4x)) sech" (In(4x)), I) y = tanh (In(4.x)) [y

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Q: hy's mea x) = eX

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Q: Differentiate implicitly to find dz if xz + In(xy) + = 10.

A: Given an equation We have to apply the implicit differention to the equation

Q: Differentiate y= 3-carhx tespect to X 6+ Sinh x

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Q: Use an appropriate substitution to integrate 12 x*(x++ 1)°dx

A: The given integral is 12x3(x4+1)9.

Q: Differentiate y= cosh vx

A: Given, y = coshx  We have to differentiate it.

Q: How do you slove this differential eqaution? y'' + 2xy = y

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Q: dy by implicit differentiatio Find

A: According to the question, we have the the equation,x7y-xy7=8we have to find dydx so,

Q: expanded as odulus of x, the 1-e

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Q: ] Integrate by parts to show that Vx dx = 2e4 - e* dx. ex. е —

A: To evaluate the given integral choose  √x as the first function and ex as the second function and…

Q: sE de = 6 - +- + arctan( )) +c %3D 1+ Vx

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Q: Use differentials to approximate the quantity   √99.7

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Q: 3. Stanh3x dx = Jsinh3x, Ssinh3x_ dx %3D u = cosh3x du = %3D

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Q: d y' of y= In(tanh2

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Q: 1 1+9g2 dæ| dxl

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Q: Approximate the sol of x = sinx upto 4 decimal places by using Newtons method.

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Q: Find the geneul suluticn dy t. + 2y= 2X 2. dx

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Q: Differentiate. y=de* +6 dx

A: Given y=ex+6

Q: ㅠ -π sec xdx. 3

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Q: Use integration by parts to evaluate /(3x+2) cos (2x)dr.

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Q: Evaluate 4 dx V4-x2

A: To find out the integration.

Q: Differentiate. y = In (7x + 8) In (8x + 5) dy dx II

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Q: Differentiate, and make sure to show all your work: 3z ²-2 Y= 5 cosh z

A: We have to differentiate the given expression, y=3x2-25cosh x Apply the quotient rule for…

Q: Find y't yu 4=In(sec 9x +tangx)

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Q: Find where where y = V5x + sech¬1 x + In (tanh(x² + 3)). dx

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