2. If y = x2 + 2 and u = 2x – 1, then du II

Q: Solve the general solution of the given DE: dyldx = (2y/x) + (3x/2y).* %3D

A: Suppose any linear differential equation can be written in the form of  dydx=fyx then it is a…

Q: 10. If z = x + f(u), where u = xy, show that dz = x. х дх

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Q: 4. If u = xy + y²z³, where x = rset, y = rs²e when r = 2, s = 1,t = 0.

A: We have to find solution

Q: € 4. If y=u² and u = x³ + 4 determine dx

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Q: 5. Find a general solution to the Cauchy-Euler equation x?y" + 7xy' + 9y = 0, for x > 0.

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: If the rst line has the form Ax + By + C = 0 and the second line has the form Dx + Ey + F = 0 and…

A: Given,  The first line  Ax + By + C = 0  and  is to pass through the origin  The second line  Dx +…

Q: If z = In(x² – 2y), and x=u+v, y= e" , find and du If w=2xy'z', and y =x² +1, z= Vx, find dx

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Q: fong=メーm X= Sin z0 4= coszo COSzo df =

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Q: - If W = xy + y2+1 azw Show that a2w ey %3D дхду дудх

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Q: Let z=xIn(x²+y²-e)-235xy, x=te, y=est. If the value of oz when s=2 and t=1 is equal to Ae?+Be", then…

A: Here, the given functions are: z=x lnx2+y2-e4-235xy, x=t es, y=est so, z is a function of x and y…

Q: 15. In AXYZ, XY YZ and m/XYZ = 46*. %3D 46

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Q: Find.: if dy æ*y+æz – yz² = 7. - -2y: 2yz-z C. E. None of the others. /Geen van die ander nie. 비 비…

A: Given; x4y+xz-yz2=7

Q: .3 If U = 2 – x, | x/2- xdx= = n} .3 -J uvūdu В (2 – u)/ūdu | .3 © (2- u)/ūdu 1 (D uvūdu A)

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Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: Solve the following problem du = 0 ; x € (0, 1) ,t > 0, u(0, t) = u(1, t) = 0, u(x,0) = %3D %3D

A: Given partial differential equation is, uxx-ut=0       ..............1 With condition u0,t=u1,t=0,…

Q: Suppose E(X) = 2, V(X) = 4, E(Y) = 6, V (Y) = 8, and E(XY)= 10. (1) E(X +Y) (2) V(2X +3Y) (3) V (2X…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: If x= 2u3 – 3u² and y=u³ – 3u, then dy is dx u+1 (A 2u u+1 B и — 1 2u и — 1 D

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Q: (b) If z = 9t²e 4, find dz dt 4

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: dw и and if w = x³ + In (²) dv E) + y, x = u² –" + 5 and Find - ди y = 3v + 5u and point…

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Q: Compute |// a² d.x dy dz, where E = {(x, y, 2) : x² + y? < 1,0 < z < 1}.

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Q: Solve. a) y - e" cosy b) +2y= + 2y 6e **-+(Let u - )

A: Since you have asked multiple subparts of this question, we will solve the first three subparts…

Q: (a) Suppose x E Q with x # 0 and y E R – Q. Show that their product ry is irrational.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (b) If z =W, show that: x- y xy 0 =

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Q: If y = x2 +1 and u= Vx? + 1, then at x = V3 equal to du 1 -4 -1

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Q: If a > 0 and [[ 20*+v 20+u° dr dy = 1(e* – 1) , a =?

A: Using polar coordinate evaluate the above integral

Q: 3. (z, y)(1.5x, 1.5y) A' will be located at ( B' will be located at ( C' will be located at (

A: We have given the scalar factor i.e . (x,y)=(1.5x,1.5y)

Q: (1,1) S[3x*+5y+i(x°-y°)] dz along y=x Evaluate (0,0)

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Q: y' + 2y = x³e-2x

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Q: If i = xi+yi+zk then grad (r") is equal to

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Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

Q: If y= In Cschx + coth y Biod dy

A: Given: y=lncschx+cothx

Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: 23. If exy = 3, then what is Y at the point (1, In3)? dx -In3 3ln3 In3 -4In3

A: Given:- exy = 3 To find:- dy/dx at point (1,ln3)

Q: T (x, y) (2x,y) is an is %3D

A: T(x,y)=(2x,12y) The transformation of any figure changes the size, shape and the position to create…

Q: Given y = Va In æ , what is dy dr In z+2 In z+y7 dy dr dy dr In z-2 dy In z-I dr ||

A: Given,

Q: In(y) 6° Evaluate dy.

A: Consider  I=∫19ln(y)ydy

Q: . If 4=(x+2y+az, bx-3y-z,4x+cy+22) is irrotational. Find constant a,b,

A: Follow the procedure given below.

Q: If y = In(x² + y²) then the value of d at the point (1,0) is %3D Select one: O a. 0 O b. 1/2 O c.1 O…

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Q: Prove that the general solution to L(y)=(x) is y=Yh+Yp

A: Definitions:  yh is a homogeneous solution so, for any yh, Lyh=0.  yp is a particular solution so,…

Q: 3. If (x, y, z) = xy²z find grad 6 at (2,−1,3).

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Q: In GL(2, Z,,). det

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Q: Perform the necessary operations to solve the following. Given z1 = 2 + 4i z2 = 5e21 Z3 = 4 cis 40°…

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Q: (1,1) Evaluate [ (3x²+4xy+ix)´dz along y=x² (0,0)

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Q: 4 Ruret MC w co , , d, 7 the y a Fid e co f de

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Q: 5. If y = In(x + y), find y' at the point (x, y) = (e – 1,1).

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Q: Let z=xin(x2+y²-eª)-162xy, x=te°, y=et. If the value of when s=2 and t=1 is equal to Ae?+Be", then…

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Q: 7) If z(x,y) = x² + y², x=u+v, and y=u-v, find dz du

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Q: Prove that eª (x – 1) = + +c is a solution to xy dx + (y+ 1)e¯ªdy = 0. 2y?

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.