* = Y, ÿ = –2x – 3y à = 3x – 4y, ÿ = x – y • i = 5x + 2y, Ý = –17x 5y

Q: 4. f(x, y) = 5xy - 7x² - y² + 3x − 6y + 2 5. f(x, y) = (xy − 1)² 6. f(x, y) = (2x - 3y)³

A:

Q: Зх +8 (y-3x) dydx y + 5x —1 ) — 5х (y – 3x)"

A:

Q: {3x+y=-3 2x+3y=5 (X,y) =

A: Given: 3x+y=-32x+3y=5 To Find: The value of x,y.

Q: y2 = 20x О А. (5,0), х - -5, у-аxis В. (5,5), х%3D5, х-аxis С. (5,0), х%3D — 5, х-аxis D. (0,5), y…

A: Given query is to find the the focus , directrix and symmetry for the parabola.

Q: 17. y"-5y6y=t² + 7, y(0) = 1, y'(0) = 0

A: For an initial value problem with boundary conditions available, we have to convert the given…

Q: 2y" +2y=2sinx y(0)=0, y'(0)=1

A: Solution y=CI+PI CI=Characterstic integral PI=Particular Integral P.I=sin xD2+1Let D2=-α2so…

Q: 1 5earctan(y) dy -1//3 1+ y2 3 1+ у2

A:

Q: y" + 2y'+ y =t O y = t-2 O y = 1/2 (t) O y= t O y = 2t -1 O O

A:

Q: Q. / Standx dx 3 None 2log|sec4x| + c 3 8log|sec4x| .+ c 3 2log|sec4x| + c 4

A:

Q: Solve the system.

A: Consider the system of equations 2x-3y=4                                           ......(1)5x+4y=1…

Q: 4x + 4y + Z = 16 5x - 3y -27 5x +y+ 2z - 31 %3D N.

A:

Q: Min 3x + 2y + Z x+ 4y + Z27 2X + y+ 3z 2 10 X, y, z 2 0

A: The given problem is: Minimize P=3x+2y+zsubject to the constraints:x+4y+z≥72x+y+3z≥10x,y,z≥0…

Q: 2) y' – (cotx)y = -(2cosx)y2 %3D

A:

Q: find ƒx , ƒy  . 1. ƒ(x, y) = 2x2 - 3y - 4 2. ƒ(x, y) = x2 - xy + y2 3. ƒ(x, y) = (x2 - 1)(y + 2)

A:

Q: ① y" +16y=ex y-y-6y=2sin 3x ly-y-2y=3x+4 4y" +4y+y=3x² グッ 2

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

Q: 4-y² 2-y SŠ *-* zdxdzdy

A: Given:  Let I=∫02∫04-y2∫02-y z dx dz dy To Find: To evaluate the given triple integration.

Q: y" + 4y'+ 20y = 23sin t – 15cost y(0) = 0 , y'(0) = -1

A:

Q: 3. x + y = 20 y = 5x + 2 6. 4x - y 5 y =- %3D 4x + 1 %D 9. 5x---16 4y %3D 12. 10x 2y 9.

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

Q: Find ƒxx ( x, y)  and ƒxy( x, y). ƒ(x, y) = -3x2y3 + x3y

A: Given that, fx,y=-3x2y3+x3y Then we get,…

Q: dy If y = ( a² +1) (x³ + 3) dx %3D O 5x^4 + 3x^2+ 6x 6x^3 O 2x + 3x^2 O 2x^2 +2x+ 3x^5+9x^2…

A: Question 1,Given,            y=x2+1x3+3To find: dydx

Q: YQʻ +y² = x 1-2xy2 2y(x2+1) „y' :Select one True False

A: Differentiation

Q: y" +2y'+ y = t O y = t-2 O y= 1/2 (t) O y = t O y = 2t -1

A:

Q: -x+y+2z = -3 3x- y+z = -2 2х- Зу- 42 %3D 1 X = y =

A:

Q: Find: 군x, 군y, Zxx , 군ys, 군xy, 2sx = X+y Xy-1 Z =

A:

Q: 23- y" + xy = 0, y' (0) = 0, y' (L) = 0

A:

Q: -2 Evaluate (5y- 2)dy

A: Given problem :- Evaluate∫125y4-2dy

Q: y'+2y/x=x, y(1)=2, y(2) using h=0.1

A: given :y'+2yx=xy(1)=2, y(2) using h=0.1

Q: Given: xIn y + y²z + z² = 8 Find: дх дz -(x + 2y² z) y(y² + 2z) -y ln y x + 2y² z - In y у2 + 2z -у²…

A: Let's find derivative of given function.

Q: 3 (x²-2y+xz) dydzdx = 0. -2 1

A: see 2nd step

Q: 4 X ~Y -Z -Zx+6y+2 =9 こ 4イ X -

A:

Q: X + y + z = 11 X - y + 5z = 17 5x + 5y + 5z = 19

A: See the details solution in below

Q: X 3Y + Z = 33 -X+4y - 22 = -47 2X-y+ 2z = 26

A:

Q: find ƒx , ƒy  . 1. ƒ(x, y) = 5xy - 7x2 - y2 + 3x - 6y + 2 2. ƒ(x, y) = (xy - 1)2

A:

Q: 2y + z = 1 29. у + 2z 3D 5 y (x + y + 3z = 8

A:

Q: d. {(x, y)| y = 3x – 8} {cx, y)ly = } x+3 е. %3D x-5

A:

Q: Solve the system of linear equations.

A: Solve as matrix equation AX=b

Q: 1. y+ /x + y = 2x at ( 2, 2)

A: Follow the procedure given below.

Q: (18) y "+9y '= sec² 2x %3D (19) y "'+6y "–14y'–104y = -11 le*

A:

Q: Solve the system of linear equations.

A:

Q: 2x + y 5z - 4y Find the total ditferential. W = 5z + 8x 10x + 5y 2 -x+ 5z – 4y dw = (5z – 4y)2" (5z…

A:

Q: y" +2y' + y = t O y = t-2 O y = 1/2 (t) y = t O y = 2t -1

A: To find the particular solution to the given differential equation first write it into operator…

Q: Solve the system.

A: Solve the system.

Q: 2x y'' – 3y' – 10y = 7e y(0) = 1, y'(0) = - 17 - %3D %3D

A:

Q: roblem. y" – 2y' + 2y = e-; y(0) = 0, y'(0) = 4 %3D

A:

Q: 2X + y - x - 2y + 2z = -11 3x - y + z = (x, y, z) =

A:

Q: 2x+y-52 +l =. X-y+ 2-6= 0 4x+zy-32+8 =

A:

Q: x+y-z=6,3x-2y+z=-5,x+3y-2z=14

A: Given equations are: x + y - z = 6 ............................ (1) 3x - 2y + z = - 5…

Q: Evaulate: •2 •1 px+y (2y)dzdydx 0 Jo Jo

A:

Q: y"+5y"+8y'+4y=4x+eX y(0)=0, y'(0)=1, y"(0)=-1

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.