Problem 01: (a) Write down the general form of the Cauchy-Euler differential equation of order n. (b) Solve the following initial value problem: d?y dy x2 dx2 4х + 4y = 4x2 – 6x³, y(2) = 4, y'(2) =-1 dx

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Q: Use Thieoi to find (E)}. (Write your answer as a function of s.) f(t) = 3t2 4 sin(5t) L{f(t)} = %3D

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Q: Find the area of the triangle with vertices: Q(4,-1,4), R(6,0,6), S(8,-4,7).

A: To find  The area of a traingle with vertices. 

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Q: Find the optimal Solution or optimal solutions for each of the following linear programming problems...

A: Given,         Max(Z)=40X1+80X2S.T.     X1+2X2≤60   4X1+3X2≤20and X1, X2≥0

Q: 7(xe* +e*)sin(xe*)–14sin(x)dx

A: Evaluation of the indefinite integral

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Q: Which of the following groups are solvable groups: Z/nZ, D8, and S4.

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Q: Find the equation of the following conic in GENERAL form. 1. Circle that is tangent to the lines x=...

A: Consider the equation of the circle is x-h2+y-k2=r2 where h, k is the centre and r is radius. It is ...

Q: 3y-8 and x2+2y%3D0 is rotated about y-10-D0

A: We have to find the volume of region.

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A: As given in the question

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Q: Ra0+Q = E(t). dt

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Q: 5.6) Apply the integral test to the series 1+e2n n=2

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Q: 5. Prove or disprove each of the following statements: (a) Any set of 7 distinct integers contains t...

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Q: 7-52. Curves to parametric equations Find parametric equations tor the tolowing curves. Include an i...

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Q: 3. In each case suppose R" has the norm ||l inclusions: = max {ril,., r.}. Prove each of the set (a)...

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Q: If E an is a convergent series with positive terms, is it true that the series ( a) Σ(1+ α) (b) Esin...

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Q: c) What can you conclude about this series? Select all that applies. O The series converges because ...

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Q: Use the integral test to determine whether each of the following series converges or diverges. For e...

A: To determine whether the given series converges or diverges using the integral test.

Q: #12 only

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Q: 1 4 2 3) Find the null space of the matrix A = |0 L-2 1 1 -1 -8 -4 -2

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Q: Find the distance across the laké in each diagram. 23)

A: 23). Given,                  

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Q: X+x-5 Find lim 1-2x-x'

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Q: Find the volume of the solid inside the sphere x2 +y2 + z2 = z and the planes z = 0 and y + z = 1. S...

A: First, we will be sketching the solid inside the sphere x2+y2+z2=z, the planes z=0, and y+z=1. Now,...

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Q: Determine whether S = {(4,3,2), (0,3,2)(0,0,2)} is a basis for R³. If it is, write u = ( 8,3,8) as a...

A: We have to determined whether S=(4, 3, 2), (0, 3, 2), (0, 0, 2) is a basis for ℝ3 or not. also we ha...

Q: dy 2. - (x +3y – 2)? dx

A: Solve the differential equation, by substitution method

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Q: ala lo oepse a ad 1. Let m*(A) = 0. Prove that for every B, m*(BUA) = m"(B).

A: We have to prove the given statement.

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Q: qu2 .01 ai anoitoni lo oonoupse a od (A oels bnnI.031 moitonl s of 1. Let m*(A) = 0. Prove that for ...

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Q: A bag contains three red marbles, two green ones, one lavender one, two yellows, and two orange marb...

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Q: A small cannonball with mass 9 kilograms is shot vertically upward with an initial velocity of 130 m...

A: we have m=9, v=130, k=0.0025, g=-9.8

Q: 2) Min(Z) = 4X1 + 6X2 S.T. 5X1 + 10X2 12 X1,X2 20

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Q: a2/ Using Newton's divided difference fonmula, find the missing value from the table: 4. 6. 14 15

A: Solution

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A: P-series test

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A: The direction ratios  of lines perpendicular to the yz-plane are 1,0,0 We obtain the equation of lin...

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.