The largest interval for which the IVP: (In(e* – e)) y' + y = 1, y(5) = 0 %3D X-6 has a unique solution is (e, 6) O (1, 6) O (In (1 + e).6) (In (1 +e). ) O(1, 6) (2; 6)

Q: c1x1(a) + c2x2(a)+ . . . +cnxn(a) = x(a). Let X (t) be the n x n matrix with column vectors x1, x2,…

A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: ■ If y = Σº。 (k + 1) x²+³ then y² = 0 k=0 k=0

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Q: Is g = {(x, y) ∈ [−5, 5] × R : x^2 + y^2 = 25} a function from [−5, 5] to R.

A:

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A: Given; if y = x6x , then y'(1)=?

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A: Solve the differential equation for arbitrary constant c:…

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A:

Q: y = In(x vx? + 1) ; find y' x2+1 2x2+1 y' = y' = %3D x (x2 - 1) (x2+1) O Option 3 O Option 2 2x2+1…

A: The given function,  y=lnxx2+1

Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

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Q: (4x + 1)2 x2 - 5 Find S' if s = s' =

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Q: (3) y'= y(3-y), y(0) = 2.

A: To solve the following initial value problem (IVP).

Q: -x)y' + y = x²e²x, x>0, V₁(x) = 1 + x, -3)e²x + 1)e²x -x²)e²x - 1)e²x - 1)e²x

A:

Q: A third order linear, homogeneous DE whose general solution is  is: y(t)= c1e^(t) + c2e^(2t) =…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 1. If y = In(V x² +1 ) , then y' = 2x (b): 2x (a) x² +1 3(x2 +1) () 3(x2 +1)-2/3 (d) 3(x2 +1)

A: y=lnx2+13⇒y=lnx2+113⇒y=13·lnx2+1   ∵lnxy=ylnx

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A:

Q: If f (x, y) = Vr³ + y³ In(x² + y²)e*in (zy+y') + x³y+ 10 , then f. (1,0) =

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Q: 2(1-z) Evaluate S S --) dy dx dz

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

Q: If f(x)=e4x+6, the linear approximation L(x) of f(x) at x=In(4) is OL(x)=e6(1+44(x+In(4)))…

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Q: Consider an AR(2) model: x₁ - x = (x₁_₁-x)+₂(x,-₁)+z,, where z, ~ - wn(0,0?)... ¡ – ¦(¹− Â₂) and ♣…

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Q: - 24 - 17/ 42 DE ETEEAP Name Exercise 6 Find the general solution of 1. y' = x -2xy

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A: Consider the given system of differential equation as: x'=351-1x

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Q: Sxª+a*+ a®) dx = %3D O a. xa+1 ax +C Ina а. a + 1 O b. xª+1 a + 1 ax +aªx +c Ina O c. xa+1 +а\ina +…

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Q: The largest interval for which the IVP : (In(e* – e²)) y' + y = 1, y(5) = 0 х —6 has a unique…

A: We need to find the largest interval for which the given IVP has the unique solution.

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A: Here is the solution of the given problem.  By using derives under Integral.

Q: If x'y" - 3xy' +3y = 0, y1 = x,y2 = x³, y(1) = 3 and y'(1) = 0 then c1 and cz (a) C1 = 3, C2 = -1…

A: (e) None of these

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Q: Which of the following differential equations are separable? dy (1)(1+2y²) = y cos x (ii) (e* +…

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Q: 5. By Chain Rule , evaluate b. y' for y = u² + 2u and u = x² + 2 %3D

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Q: (-2m*)' (2a'6') (32y 13. 14. 8m (2ab*)' 15.

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Q: dife equa Oʻu 4. -+X- +x +18 2

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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.