If z =3+2t. y=-t,tez, are the solutions for az + by - e, a, b, c, z, y € Z, then the number of positive solutions is a. 1 O b. infinite None O d. 2 Oe 0

Q: Let y(x) be the solution for the DE: y = (x + y-1)? If y(0)– 1, then find y() 3元 O 2+7 O8-7 O 2-7

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Q: Consider the following IVP: 1. y"+a2y = 0; y(0) = 1, y'(0) = 0

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Q: The values of C, and C2 so that y(x) = C, e²x + C, e-2* satisfies the following conditions: y(0) = 1…

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Q: Let y (4)-y ""=1+ 2e*. Then we can write a suitable form of a particular solution as: Yp= Ax + Bxe…

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Q: Find a particular solution of (15) y′′−3y′−4y=−8etcos(2t).

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Q: 3. For what values of to and ro does the IVP: x' = 2/r, x(t.) = xo, have a unique solution?

A: Given: The initial value problem x'=2x, xt0=x0

Q: solve the Riccar' equanim 3 yoing the green partienten soluhon y'ax) + 1 y ₁x) +y²cx) = 4 ca).…

A: Riccati equation

Q: Which of the following is a solution to xy" + y' = 0 ? y = = 1 y = x3-x O A y = In x %| O D В

A: A function y = f(x) is said to be solution of the given equation  xy" + y' = 0  ...(1) if  y = f(x)…

Q: For az _and _and_ _and_ X= y = z = = z' For a = Or there are no solutions. For a = Or . X= y = z =…

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Q: For which values of a, b, and m does x + a = b have a solution in Zm?

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Q: Given that (z-N(z-n=6z-221, where z=x+yi and z is the conjugate of z. Solve for x and y 28 and y=3…

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Q: If y=e' is a solution of the DE: ty"-2(t+ 1)y'+(t +2)y=0 Then the general solution of this DE is :…

A: The given differential equation is: t…

Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 4y = 3e³t Y(t) =

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Q: Show by direct substitution that (-1)"+1 y = n-1 is a particular solution to (x + 1)y" +y' = 0

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Q: Let y" + 2y' +y = 17e*. Then we can write a suitable form of a particular solution as: O None of…

A: Let's find.

Q: If v,=e is a solution of the DE ty"-2(t+1)y (t + 2)y=0 Then the general solution of this DE is:…

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Q: Which of the following is the solution of ди +2- ди Ox 0 = a) u(x,y)= e"-2x b) u(x, y)= (2x + y)³ c)…

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Q: Following the method performed in the videos to solve 4y" + 8y' + 3y = 0, we seek find the m…

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Q: 2. Jr.,(x) + Jvo, (x) = 2Y Jv (x) Ju (X) I need two examples to prove this property using the same…

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Q: Find a particular solution to y" + 6y + 8y = -7tet.

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Q: 2. Find the general solution of d'y d'y + 12 dr Sy 21e dr

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Q: The solution of the following IVP:y'=y³ x e*, y(0) = 1 Select one: O a. y=V4-2 ex2 O b. 1 V2- ex? C.…

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Q: Determine whether the following statement is true or false. is a solution of the IVP eYdx- edy D0;…

A: To solve the given differential equations and state whether the statements are true or false

Q: Find a particular solution to y″+36y = 60sin(6t).

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Q: Let y(x) be the solution for the DE: y (x + y +2)² If y(0) = -2, then find y() 7- 3 4 2+ O 8 JTO 3…

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Q: What values of z and A make y=Acos(zt) a solution to y''+3y=0 such that y'(1)=1

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Q: evaluate x tr20 +xt/2 /x+)=3, dekimnt the vahie of d: Bocs C3 x?+ Ax † 3y 0, have a sclution if yes…

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Q: y(4) + 3y" + 2Y = 0

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Q: Solve the following IVP: (2et у" — 25у %3D to 0) y(0) = 0, if 0 4 y'(0) = -1. Letes SUNITT STED…

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Q: Find the solution of the following problem: Uu = Uga I> 0, t>0, u(x, 0) = 2 u(0, t) = 0, t2 0. - z,…

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Q: 6 - Show that x(t) = (C1 + C2t) e¬t is a valid solution to i + 2yi + 7²x = 0.

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Q: From a given instance of x=0 and y=3, determine where the solution od this DE. (2x-y)+(2y-x)y'=0 is…

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Q: 4. Find the solution of the following DE: a. y(5) + 5y(4) + 10y(3) + 10y" + 5y' + y = 0

A: Given differential equation is: y5+5y(4)+10y(3)+10y''+5y'+y=0 Write auxiliary equation corresponding…

Q: Show complete solution

A: follow next step

Q: Show that if Ax = b has more than one solution, then it has infinitely many solutions. (Hint: If x1…

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Q: If y, =e", y2 =te are solutions to y"+b y' +c y = 0, find the values of b and c.

A: Given: y''+by'+cy=0y1=e4t ,y2=te4t

Q: If P(2) = z³ – 3z² + qz + 100 and z = 4 + 2i is one of the solutions of P(z), which of the following…

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Q: If P(z) = z3 – 3z2 + qz + 100 and z = 4 + 2i is one of the solutions of P(z), which of the |…

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Q: Consider the following IVP: y" + 3y' + 2y = 12x²; y(0) = a, y'(0) = b Find the solution. A y(x) =…

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Q: A. If:Z = x + iy, Solve the following equation to find x and y: 4x+ y_ 4y+14 -0 then use Demoivre's…

A: Given: - If Z=x+iy and the equation is, 4x+y1+ix-4y+i4iy=0 To find: -The value of x and y. Then use…

Q: Given s= 6x7x20: Find a) whure y is ot eauilibrium 5) where is imereosing ) whee y is docieasing

A: we have ,  y'=6x2+7x-20 ...........(1) we have to find,  a) where y is at equilibrium.  b) where y…

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

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Q: 3. The solutions to P(x)=0, in simplest exact form, are z = -2, -d±eVf. The values of d, e, and f,…

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Q: Consider the following IVP: y" + 3y' + 2y = 12x2; y(0) = a, y'(0) = b Find the solution. A y(x) =…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Verify that r = Cie +C2 is a solution to a" – r' = 0. Find C1 and C2 so that r satisfies x(0) = 1…

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Q: If y is the solution of the I.V.P t y"–4 t y' +6 y =0, y(1)=7, y'(1)=4, then y(2)=15. Select one: O…

A: We have to solve given initial value problem

Q: The set of all solutions to y" = 5x + e** is given by 1 a) OC,x + 16 e* + C2 4x b) O 5x + e** + C1x…

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Q: Determine the form of a particular solution (u,) of the given DE u" + 6u' + 9u = (7t + 2t )e¯*. o 4,…

A: To find The form of a particular solution of the given DE.

Q: Given that z = x² + xy, and that variables x and y depends on s and t as follows: x = s +t and y =…

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Q: The solution of the following IVP:y' =y³ x ex, , v(0) = 1 Select one: O a. V4-2 ex2 b. V =V2- ex² C.…

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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.