The solution for the IVP: Uxi u(x, 0) =2 x u,(x, 0) -ex. ux, () - 2x + (*-0-(**) O b. u(x, t)-x+(-*-20)(x*+2) 4. Oc. u(x, t)-2x Od. 1 u(x, t) - x - - (e*-2)o**20) e. 1 u(x, t)=x+ (e

Q: If y = u³ - 4 and u = 3x² + 10, find y' O 18x(3x² +10)² O 3x(6x² + 10)² O18(3x² +10)² 6x(3x² +10)² घ

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Q: そx4

A: Given: 1-2xuy+ux=0 Auxiliary equation is  dx1=dy1-2x=du0 equating first and last terms…

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

A:

Q: (z/(u + m) = d)dĒшAuA (! h) 3n3m(n+m=4^n-m=2) (1=m-uv+=+u)шEUE (8 (S=₂+₂)Ẹи (ə (0 = m+u)шEUA (³ (m>…

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Q: Max Z=3 x1+2 X2 s.to -X,+2x2 <4 3x1+2x2 S14 using Graphical Method X1-X2 S 3 X1 , X2 20

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Q: If A- A = I, then (4-1) = %3D

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Q: {In(æ² + xy+y³)} Find

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Q: If f(z) = (a") + and f(z +y) + f(z-y) Kf(z)f(y), then the 21 value of K.

A: Given that: *f(x)=ax+a-x2 *f(x+y)+f(x-y)=K×f(x)×f(y) Thus, the function f(x+y) is,…

Q: x=[-5,-4,-3,-2,-1,0,1,2,3,4,5], A= [0.45    0.61    0.75    0.88    0.96   1    0.96    0.88    0.75…

A: Given: x=[-5,-4,-3,-2,-1,0,1,2,3,4,5], A= [0.45    0.61    0.75    0.88    0.96   1    0.96    0.88…

Q: of Find (7,- 2) if f(x,y) = 4x² + 7xy - 3y? + 6x - 5y - 2. of (7,- 2) = (Simplify your answer.)

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Q: Differentiate. h(r)= 2-2r-3 9r-5 O A. h'(r) = OB. h'(r)= gr² +8r+37 (9r-5)² O D. h'(r) = 9r²-10r+37…

A: given function

Q: 4- 2. -2. -4 -6 10

A: Question is based on Observation of given graph.

Q: How can you apply the chain rule in calculus 3 with multivariable calculus

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Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: 3tan(x)=2sin(2x) from [0, 2pi)

A:

Q: giver yn f(५) ५) -2x + 3, + 2, find of ax

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Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

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Q: Compute x -1 where x =i +1 2.

A: topic- complex numbers

Q: TF x and y are orthon ormal rectors then Pind Value of Ilx+y12 - ||x-Y2

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Q: Let Var(X₁) = Var(X3) = 2, Var(X₂) = 3, Cov(X₁, X₂) = 2, Cov(X2, X3) -2, Cov(X1, X3) = -1. i)…

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Q: 31 Xi + 47 Xz + 14X3 Ex Al+

A: Given: Max z=31x1+47x2+14 x3Subject to; 2x1+3x2+x3≤4 and x1, x2, x3≥0 To find: Optimal solution and…

Q: If 6x° +x*-y? 3x² +y? if (x, y) (0, 0) f(x, y)= if (x, y)= (0, 0) then f,(0, 0)=

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Q: 2 Ⓒz² = x² + y² 2

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Q: 를 + 2 I→-5 5-+x

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Q: 1. (а) 52x $* (b) 3' x 32 - 5 2. (a) k* x k? (b) m³ x m 3. (а) у к (-у") (b) -x (-)

A: Given: 1.(a)52×56  (b)33×332.(a)k4×k7   (b)m5×m9   3.(a)y2×(-y10)  (b)(-z3)×(-z4)

Q: what values of k will

A: Given,              f(x, y)=(x+iy)2+x-ikyx+iy

Q: By using the substitution u = 4x + 1, evaluate (4х + 1) dx +x + k 4x? + x + k (4x + 1)² + k x' + x +…

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Q: sWhat are the points of discontinuity? (x+1Xx-5) y3D *+4x+3 Ox-3, x--1 Ox--3, x=-1 Ox=5 Ox=5,x=-1

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Q: Find 4 of 3xy –- x³ = 5 at (1, 2)

A: Given; 3xy-x3=5 at (1,2)

Q: Evaluate 7x 11 √(x - - − 1)(x – 3) - - - dx

A:

Q: if z=x+iy find real x and y such that |z+3|=1-i(z-2)

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Q: Linearization X = a [스 (b+y)

A: Linearization is done to obtain an equivalent linear equation for a given equation. The linear…

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: x + 5 dx = (9 – x²) + C 5 x 5 V9 - + C 9 V9 - x2 *e 5 x 9 + C 9 - x2 + C 4 9 - 18 v9 - 5 x 18 v9 -…

A: Given:              ∫x+59-x232 dx

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.