I-y+z=1 2x + 2= 2

Q: 1n. fix, y) = /3x>y – 7x³y 18. f (x, y) = x + y %3D X - y -

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Q: у"+2y' +2y -6(t- п); у(0)31, у (0) - 3 y(1) = D %3D

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Q: mation 9. y'-y = 2te²¹, y(0) = 1 2

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Q: sec² (w) - -dw 4w2 +1 10.

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Q: Vye-y" dy 2.

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Q: y = x²,y = 2 – x, x = 0 and x > 0 -

A: Let us first plot the region.

Q: -4 3t° 3t+ i dt

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Q: fc y 3 ds, C :x=t2, y=2t, 0<t<1

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Q: Sx, y) = 2r - 3y²

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Q: Solve using separation of variables:   y'-xy+y=2y

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Q: 2 y (4- y²)³ dy

A: The objective of the question is evaluate the definite integral.

Q: 2-x'y'y'+ xy' =1

A: Let's find.

Q: Solve: y''' – 3y'" – 6y' + 8y = 0 %3D y(0) = – 6, y'(0) = - 12, y'"(0) : - 54 %3D y(t) =

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Q: Solve x = x + 2y and y = 2x + y with x(0) = 1 and y(0) = 2.

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Q: f (6x?y2x)dydx y-2x)dydx

A: To evaluate the double integral

Q: /1-(r-1)2 1 dydr. 0.

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Q: 1 2e10z 3 da |3D e5z

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Q: 3x' - y = 2t; x' + y' - y = 0; x(0) = y(0) = 0

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Q: Solve IVP: y'''+4y'=x, y''(0)=1; y'(0)=0.

A: Given : y'''+4y'=x

Q: 2. Xー+y=1

A: Given, The region between the circles ,  and , .

Q: (D³ + 3D² + 3D + 2)y = 0

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Q: Solve: æy' – 5y = 4x°, y(1) = 4 y(x) =

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Q: Solve y'"+ 5y' + 4y = 0, y(0) = - 8, y'(0) = 17 y(t) = %3D

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Q: 2) Solve ² y' = y(0) = 1 %3D 2 y+ 1 '

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Q: Solve y'' y(t) = - 4y' + 40y = 0, y(0) = 2, y'(0) = - 2

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Q: (b) dr dy - у — 1 x + y+3

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Q: (i) y" — у" + 2у %3D 0

A: To find the solution of the given linear ordinary differential equation we assume y=emx (where m is…

Q: Solve for y. y' = 7x + xy; y = 5 when x= 0 y =

A: We have to solve for y for the given differential equation: y'=7x+xy; y=5 when x=0. Rewriting the…

Q: Solve y" + 10y' + 25y = 0, y(0) = 4, y'(0) = – 17 %3| y(t) =

A: We have to find the solution of differential equation.

Q: (a) x-z = 1 =D1 2х +у - z 3 3 x+y = 2 3D2

A: a) Given:         x-z=1       2x+y-z=3      x+y=2 Converting into matrix form.      10-121-1110…

Q: Solve for y. y' = 7x + xy​; y = - 4 when x = 0

A: Given,  y'=7x+xy,  y=-4 when x=0

Q: Solve y'+ 8y' + 15y = 0, y(0) = 5, y'(0) = 19 | y(t) = %3D

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Q: I, x = 4 x- 2y = 6 %3D y

A: I am attaching image so that you understand each and every step.

Q: 2. Solve y" + 2y' – 3y = 3, y(0) = y'(0) = 1. II %3D %3D

A: given differential equation is linear non homogeneous differential equation with constant…

Q: 4. Perpendicular to x - 3y = 2 and passes thru (-3,5)

A: given that a line is perpendicular to the line x-3y=2 and passes through the point (-3,5). we need…

Q: 3x – y + z = -1, -x+ 3y – z = 7, I – y + 3z = -7.

A: Given: 3x-y+z=-1-x+3y-z=7x-y+3z=-7

Q: dy - 2ry = r'²

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Q: Solve y''+ 3y' – 10y = 0, y(0) = - 6, y'(0) = y(t) =

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Q: (b) y = 11 - 2x, 2x - y = 23 %3D %3D

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Q: (D³ + 2D*)y = 0 y(0) = -3 , y'(0) = 0 and y"(0) = 2

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Q: -2 2 /y + 2 dy + √ ² [√y+2_y] dy

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Q: Yt = Yt-1 + 2yt-2(Yt-3 – 1) %3D

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Q: Solve: y'''−5y''+33y'−29y=0 y(0)=−1,  y'(0)=−18,  y''(0)=−17 y(t)=

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Q: ng through the point that is ion. 10. (-3, -2); y = x – 2 12. (-1, -6); r + 3y = 6

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Q: Solve for y 2y2-3y-13=(y+1)2

A: Solve for y

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.