Auxiliary Equation: Solve the following: 1. (D^2/3 − 6D^1/3 + 5) y = 0

Q: 3. xy + Csc (xy) + x*y' = 0

A: x4dydx+x3y+cscxy=0 given differential equation

Q: Find: dx

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Q: © Tategrate 12 dx 3.

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Q: dx 3. (x+2)Vx+1

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Q: Differentiate y = Vx+1 *

A: Differentiate:    y=x+1

Q: x3 dx (x – 1)5 y = Select one:

A: First evaluate the integral by substitute method. Then apply the limits of integral.

Q: x³ dx

A:

Q: 5 dx 3. dx, x> 25x2-9

A:

Q: A ball thrown vertically downward from the top of a building at a velocity of 64 ft/sec hits the…

A: Projectile motion

Q: 14) fx In(4x) dx

A:

Q: 4. fx(1-x) dx

A: We can find the integration as below.

Q: r10 xe -dx (x+2)(x+3)(x² – 1)

A: Using gaussian 5point quadrature

Q: x*Arcsinxe

A: we have to find

Q: Solve in variation of parameters y´´ + y =cscx

A: Given differential equation is: Solution of differential equation is sum of complementary function…

Q: 1) I ftet dt

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Please solve number 8. Show the complete details of your solution. Enclose your final answer.

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Q: First 120 km of the road the car is moving at speed rate of 90 kph. Next one hour and 15 minutes the…

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Q: would I solve thi

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Q: How to solve linear Diophanfine equation

A: See the attachment

Q: Зу" — бу' + 6у%3D е' sec x

A: Given differential equation, 3y''-6y'+6y=exsecxy''-2y'+2y=13exsecx

Q: A raindrop falls into a puddle and causes a circular ripple to spread out. The radius of the ripple…

A: Ripple is perimeter of circle after 6 seconds

Q: y = x^Arctan *(x4)

A: We have to solve derivative

Q: Explain why you can omit the constant of integration when finding an integrating factor.

A: Constant of integration is omitted while finding the integrating factor because when the integrating…

Q: sec 180⁰

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Q: solve parameter method J-yこ cosh x y"-

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Q: V5/2 V5 – x² dx V5/2

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Q: ly to grow to $6540 40 mont

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Q: y = Arctan (2x)

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Q: 9. Differentiate y = /sec³ (5t2)

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Q: ди ди x====u+Yay ?х

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Q: very

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Q: Explain the concept of integration and give a real life example.

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Q: 1 l0a) Show that x²+2x+5 -dx =

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Q: PLEASE ANSWER ITEM NUMBER 10 ONLY. DIFFERENTIAL EQUATIONS.

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Q: 5. x?e-3x dx

A: ∫x2e-3xdx

Q: 3. 43. dx 2 - x (1,0)

A: 43) We have to solve the following differential equation at the point (1,0). dydx = 32-x

Q: Express the mathematical relationship between stress and strain in case of elastic material.

A: The mathematical expression can be related as:

Q: The half-life of erbium-160 is 1.191 days. If a sample has a mass of 500 mg, find the mass (in mg)…

A: Given half life  t12=1.191 days and initial mass  A0=500 mg

Q: dx 2/3 Thtegrate -27 3)

A: Given: ∫-278dxx23 To determine: The value of given integral. Formula used: ∫xndx=xn+1n+1+C

Q: the length of a rectangle is increasing at a rate of 2 feet per minute, and its width is decreasing…

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Q: for dx

A: Given integration is : ∫exdx To find the value given integration by parts.

Q: y = In(x + 3)4

A: As u mentioned to solve 2nd equation, the solution of the same is attached in next step.

Q: Use the variation of parameters method to solve y" + y = secx.

A: A differential equation is given. We need to solve it by variation of parameters.

Q: 24. y = e-, y = 0, x = 0, x= 1

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Q: dx (x² +2)

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Q: Solve for X - In (+6) - In3= h v %3D

A: To solve for x.

Q: 1 dx, x3 – 1 (b)

A: a3-b3=(a-b)(a2+ab+b2) first we will do then partial fraction then calculate the integration.

Q: Evaluate In(3 + j4)

A:

Q: escape velocity

A: We shall assume an initial velocity in a radial direction so that the motion of the particle takes…