Expand x?y + 3y – 2 in powers of x + 1 and y – 2. (up to third degree terms).

Q: 5) Find the general solution by using reduction of order method to (x² + 1)y" – 2xy' + 2y = 0 given…

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Q: 2D² +3D– 2)y = 0

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Q: 10 X =1.2 is to be sol he initial approxima

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Q: (x2 – 1)y" – 2xy' + 2y = 0 - tion ofS the o uation

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Q: Find the general solution of each ff Higher-order DE using Reduction of Order  1. (2D2 + 3D -2)y=0

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Q: (n² – 3n – 21) ÷ (n –7) -

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Q: Residue of at z = -3 is (z+3)² Select one: a. -2 b. 2 C. 3 d. -1 е.

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Q: x2+1 =0 Has soluion in R

A: Solution:

Q: Obtain the general solution valid near the origin: 2y" + 9xy' − 36y = 0

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Q: 2 (ii) using Convolution theorem. (s+2)(s²+9)

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Q: Find the general solution of the following DE in explicit form. y' =2+2/y-2x+11

A: Solution: The differential equation is y'=2+2y-2x+11 Suppose that v=-2x+y so that y=v+2x Then,…

Q: Find the general solution of the following DE in explicit form. y'=2+2y-2x +8

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 3) FIND A PARTICULAR SOLUTION OF THE ODE y"+8y-20y = 2x +5 - e?X %3D

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Q: (5 + 6t)7 16x* +6sec(x) x-3cos(x) In(x2 – 1) 2e3x + ex³

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Q: 3.Eliminate the arbitrary constant on the given equation: xsiny – x²y-3 = C

A: In this question we have to eliminate the arbitrary constant on the given equation.

Q: Find the root of f Ca) = as +bx°+ dsinx between Xe2 and x =4 with the use of 4- Bise ction method a=…

A: Suppose the root of the function fx lies in the interval xn-1,xn. Use the following formulae, to…

Q: .(1) t is straightforward to show that y = k-1 is a solution to the homog quation

A: Given,                yk+2 -2k+1kyk+1+ kk-1yk=0         (3.151)and       yk+2 -2k+1kyk+1+…

Q: ker(A) = R104 %3D O ker(A) = {0} %3D ker(A) cannot be determined from this information

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Q: 5. EB = 33, BD = 5x - 10 and ED = 9x + 3. Find x. %3D O 2.9 5.8 OOO

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Q: 5. (a) sech 0 (b) coshl1

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Q: Q:2: a) Find implicitly, if y²cosy +x² = 2xy

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Q: Find the general solution of the following DE in explicit form. y'=2+2/y-2x +7

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: :Find the first 3 terms for (1 (-1)*1 (2n – 1)!J n+1

A: We have to find the first three term of the given series.

Q: Evaluate the integral. S. 3n/4 -8 csc 2 x dx T/4 Select one: A. 16 В. 8 C. 0 D. -16

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Q: Ym - 21 , prove that + (n? m² ) yn =o 2 + (2n+1)x Ynts

A: Given y1/m+y-1/m=2x To prove that  x2-1yn+2+2n+1xyn+1+n2-m2yn=0 Solution :  y1/m+y-1/m=2x…

Q: Given that y,(x) = e²^ is a solution of y" - y' - 2y = 0, use the 2x Reduction of Order formula to…

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Q: 1. Rewrite c(x) x² +5x+2 in the form y = p(x) + r(x) where r has degree less than b. x-3 6(x) 2.…

A: The objective of the question is rewrite the given equation and end behavior.

Q: A second solution y2 for the DE x²y" – 4xy' + 6y = 0, can be obtained by reduction of order with the…

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Q: 3. Derive the reductive formula for S sec" (x) dx.

A: We will find out the required solution.

Q: a) Prove If he Given DE Is exact or non-exact Find its General solution

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Q: 12. Find the general solution using Reduction of Order: a) y"= 2ln x b) y" + y' = cos 3x

A: We have to find the general solution: y''=2lnx. Here, the value of y1 is not given.

Q: 5. Show that the formula for the Secant method can be written in the form xn+1 = [f(xn)xn-1…

A: Secant Method: Consider, y = f (x). Let, x0 and x1 are two initial approximations for the roots of f…

Q: :Use inverse matsix (by Gauss Jordan an Elimination) to solve the syálem 2x + By +3 = - 1 %3D 2x…

A: Consider the given equations 2x+3y+z=-13x+3y+z=12x+4y+z=-2 The given equation can be written as AX=B…

Q: 3. Given that y,(x) = x is a solution of xy" + 6xy' - 6y = 0, use the %3D Reduction of Order formula…

A: We have to solve given problem:

Q: Find the general solution of the following DE in explicit form. y' =3+2/y-3x +12.

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Q: 2t dt (t – 3)2

A: given integral I =∫2t(t-30)2dt

Q: Expand xy² + 2x – 3y in powers of (x + 2) and (y – 1) upto third degree | terms.

A: Given ,  f(x,y) = xy2 + 2x - 3y  By Taylor's theorem  f(x,y) = f(a,b) + {(x-a)fx(a,b) +…

Q: -3 Show that y(x) = -9x7 is a solution to 4x²y" + 12xy' + 3y = 0 for x > 0. %3D

A: We will show in step 2.

Q: z/(z-3)2 dz ; C: |z+3| =3 slove by residue theorem

A: The given integral is,

Q: The fourth term in the expansion (2r + y)' is

A: The equation for the combinations n taken r at a time is equal to Crn=n!n-r!r!.  The continued…

Q: Use the substitution y = xm to find the general solution to: x2yn - 2xy' - 4y = 0. Show all of…

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Q: 32 1 xy+- |dydx Evaluate: 2 1

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Q: 4. If LM = 41 - 2r and NP = 7x + 5, find LM. %3D

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Q: 2. -4 ) 3x-3x that sahisfies y1)=0 Find the Solhion to

A: We need to solve y'x=3x2-3x-4, y1=0. So,                 y' =3x2-3x-4⇒y=∫ 3x2-3x-4dx⇒y=x3+1x3+c1We…

Q: x² – 6x + 8 - 4. Evaluate | I Tr? +1Xx–1) dx using Partial fractions. .2

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Q: 5) Find the general solution by using reduction of order method to (x2 + 1)y" – 2xy' + 2y = 0 given…

A: Use the procedure of reduction of order to solve the given differential equation as in next step.

Q: 1. Evaluate the following. Use only the rules and techniques of integration presented in the module.…

A: To evaluate the given integral.

Q: 3a Show that the method xn+1 = Xn 6+ Xn ,converage to vā. %3D a

A: