9. Tell whether (9, 2) is a solution of y <4x+ 1. a. Yes, (9, 2) is a solution of y < 4x+ 1. b. No, (9, 2) is not a solution of y <4x+ 1.

Q: Show that the equations x+ y +z = 4, 2x + 5y - 2z = 3, x + 7y - 7z = 5 are not consistent.

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Q: 1- If y+3y = 8 then g-solution is %3D a- y+ 6 = 1 In (8-3y) = x +c a.

A:

Q: 11. Find the particular solution of 2ydx = 3xdy, when x -2, y = 1

A: Given : Differential equation :  2ydx = 3xdy And x = -2, y = 1   To find : Particular solution of…

Q: Is (2, –1, 3) a solution of 3x + 5y – 2z = -5 2х + Зу- z 3D —2 2x + 4y + 6z 18? Replace x with 2, y…

A: Consider the system of equations. 3x+5y-2z=-52x+3y-z=-22x+4y+6z=18 And, the solution of the system…

Q: The solution interval of 2y +12≥3 or 3y 1 or y≤ -1} .B O (-∞, -1]U (1, ∞ ).CO {yly ≥1 or y<-1} DO

A: We have to find the solution interval of  2y + 1 ≥ 3 or 3y &lt; -3

Q: Solve a & b with given A[r = 3x şax+ (y + z + 3) Ay +(6x - z³) a₂] where: np = ax + 4ay - 2az 2+y³

A: Given

Q: : Discuss the existence and unique solution for the IVP y'= 3y3, y (0)=0

A: This question is related to Differential Equations

Q: 8. Find the partic ular solution of x²y" + xy' = 1; y = 0 and y' = 1/2, when x = 1.

A: We have to find the particular solution of x2y''+xy'=1 ; y=0 and y'=12 when x=1.

Q: Verify that ry4 +r - 27 = 0 defines an implicit solution of the DE dy 4ry + 2y* + 3r = 0, dr on the…

A: The function f(x) is a rule that associates or fixes a number to the particular point x. The…

Q: Consider the following IVP: y" -3y' -10y = 1, y(0) = -1, y'(0) = 2 Find the general solution. A 5t…

A:

Q: Is y(x) = C1sin2x + C2cos2x, where C1 and C2 are arbitrary constants, a solution of y” + 4y = 0?

A:

Q: 19. Show that yı = 1 and y2 = /x are solutions of yy" + (y')² = 0, but that their sum y = y1 + y2 is…

A:

Q: 14.Show that any separable equation M(x)+N(y)y′=0 is also exact.

A: Given: Mx+Nyy'=0

Q: A) (:: :) Verify that y = c₁cos(3x) + c₂sin(3x) is a solution of y' +9y = 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: 4- Find the particular solution for: 3x²y' = 5x – 6xy, x = 2 when y = 1 %3D

A:

Q: Obtain the family of solutions 1) xydx – (x² +3y² ) dy = 0 2

A:

Q: 10. Particular solution of y"-4y' + 8y = x³, when x = 0, y = 2, y' = 4

A: We have to find the particular solution of y''-4y'+8y=x3,  when x=0, y=2, y'=4.

Q: 3. Show that y = 5x2 +2 is a solution to the DE ry' +y" = 2y.

A:

Q: 10. Find the particular solution that satisfies the initial condition. my'+2y = 3x2-5x, Initial…

A:

Q: 4. Find the number of non negative solutions to x + y + z = 21. With the conditions that x > 3, y >…

A:

Q: The form of the particular solution yp for the DE (D^2 + D - 2)y = 2x - 40cos2x should be yp = Q +…

A: Let's find.

Q: Find the optimal solution. MAX Z=6X+7Y st 4X+5Y≤20 10X+7Y≤35 3X+4Y≥6 X ≥0 , Y ≥0 and an…

A:

Q: Find the general solution of: az əz 2, дх ду (1+ /z- x – y)

A: The given equation can be written as: 1+z−x−y∂z∂x+∂z∂y=2dx1+z−x−y=dy1=dz2          ......i

Q: dr a) de rcose + rsene subject to r(0) = 1 (solve by separation of variables)

A:

Q: 4y'' + 24y' + 37y = 0 @y(π) = 1, y'(π) = 0  show complete solution

A: The given differential equation is: 4y''+24y'+37y=0, y(π)=1, y'(π)=0 which is a homogeneous…

Q: Find a particular solution to y′′+16y=24sin(4t).

A:

Q: 2. Suppose that A, B, and C are three approximations for - a² – y²) dA for D = [0, 2] × [0, 2] and…

A: Given that A, B and C are three approximations for  ∬D4-x2-y2dA                   (i) For D=0,2×0,2…

Q: The solution interval of 2y +1≥3 or 3y1 or y< -11 BO

A:

Q: (7) Find the general solution to y = (x +y + 1)

A: Given differential equation is: dydx=x+y+1 Let us assume x+y=t 1+dydx=dtdxdydx=dtdx-1…

Q: 10. Particular solution of y" – 64y = 16, when x = 0, y = 1, y' = 0 %3D

A:

Q: 3. What is the particular solution if y(1) = 0 • xy' = y+ (x² + y²) ||

A: Given:- xy' = y+(x2+y2)1/2 y(1) = 0  To find:- Particular solution of given differential equation

Q: 1. Find the number of non negative solutions to x + y + z + w 16. With the conditions that x > 2, y…

A: The complete solutions are given below

Q: 4. The line 3x + 2y – 10 = 0 is perpendicular to Ax + By + 1 = 0. Find the possible values of A and…

A: Consider the set of simultaneous equations, 3x+2y-10=0………(1)Ax+By+1=0…………(2) Let m1 be the slope of…

Q: 10. Particular solution of y" - 5y' = x-2, when x = 0, y = 0, y = 2

A: To find the particular solution of given differential equation :-

Q: determine by inspection at least two solutions of the given first-order IV . 15. y-  3y2/3, y(0) …

A: Consider the given y'=3y23 and y0=0

Q: 6- Show that y = xsinx is a solution to y +y 2cosx

A: The given differential equation is: y''+y=2 cos x

Q: Consider the following IVP: y'' -3y' -10y = 1, y(0) = -1, y'(0) = 2

A:

Q: Let (x, y,) be the solution of the following equations In 2 (2x) = (3y)n³ 3Inx = 2lny %3D Then x, is

A:

Q: Verify that for x>0, (2/ /3)x³² 2 is a solution of the equation yy" =x.

A: Given:     To verify: y is the solution of equation yy''=x

Q: Let (x, y,) be the solution of the following equations In 2 (2x) = (3y)m3 3Inx: = 2Iny Then is

A: This is very complicated &amp; lengthy problem.So I can do it in Advanced Mathematics.

Q: The solution of the IVP t(t + 4)y + (t + 4) y =t, y(2) = 2 exists in the interv

A:

Q: 2. Suppose that A, B, and C are three approximations for (4 – a - y) dA for D = [0, 2] × [0, 2] and…

A: If domain D is split in four equal squares then, the graph is as shown below:

Q: 2. According to experienced baristas, the optimal temperature to serve coffee is between 155F and…

A: Let is start solving the problem step by step with the given information

Q: I have included one line of the whole solution in the questionnaire. Analyze if this included part…

A: y = ln(1-5y2 +y3) now differentiate it y' = (-10y+3y2 )/(1-5y2 +y3) here between (+) sign so there…

Q: What is the particular solution of (3y2 + 10zy²) dz + (6zy 2+ 10y) dy = 0 when a = 1 and y 2 ? Sry +…

A:

Q: 6- Show that y = xsinx is a solution to y= + y = 2cosx

A:

Q: Suppose M = max{2x for x E [0, 4]}, then the value of M is

A: The objective of the question is determine the maximum value of M.

Q: 10. Find the particular solution that satisfies the initial condition. xy'+ 2y = 3x² – 5x. Initial…

A:

Q: 1- If y+3y = 8 then g- solution is %3D a- y + 6 = 1 b- In (8-3y) =x + c 3 a

A:

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.