7x + 5y + 9z- 8t dy = 4x + y+ z + 2e-t dt dz dt - 2x + 3y + e-t - 3t = 7x + 5y+9z - 8t dt dy = 4x + y+z + 2e-t +t dt dz * = x – 2y +3z + e-t-3t = 7x + 5y + 9z - 8t dt dy = 4x + y + z + 2e-t dt dz = -2y + 3z + et - 3t * = 7x + 5y + 9z+e-t - 8t %3D dy = 4x +y+z+2e-t dt * = -2y + 3z +e-t-3t

Q: What guess would you make for the particular solution to the linear, non-homogeneous dt2 dy 4- 3y dt…

A: Particular solution

Q: 3. Find the trajectories of solutions of the systems. dr dt = -4y³ - 2y = 4x³. 4. Find the…

A:

Q: Find the partial derivatives fx (3,5) fy (3,5) for the function f(x,y)= y^2/x-y

A:

Q: The solution of (1+y²) + (t- elan-ly Y =0 is: -1n dy %3D dt Select one: a. 1 t 3D elan-ly e2tan-ly O…

A:

Q: Exercise : 4 3 a) Evaluate , S /1-х2 |1-x²-y² .-3(x²+y²+z²)² dz dydx

A: Triple integral is used to find the volume bounded by a region. There are many methods that are used…

Q: A form of a particular solution to = 2x + 3y-7 dt = -x - 2y +5 is dt O (a b)" O (7, 5)" O (2, y)" O…

A:

Q: dr = (t ) dr = (2, -1, 0) SF.dr 2 XYz1-X yJ +z°x K • <2,-1,07 SAXyZ +Xy dt 4 S4(2t)(-t)(1) +…

A: Yes answer is correct...

Q: Find all the first partial derivatives of z = 3x°y – 7r°y. (Choose all applicable answers.) O ży =…

A:

Q: d²z 2+ 3-2z = te-2t ; z(0) = 0 z'(0) = -2 dt2

A:

Q: 8. Find the first partial derivatives with respect to x, y, and z. 6xz w = 4x +3y 18xz 18yz (4x…

A: find the partial derivative as following:-

Q: (x-2)²(x³-4) y = Vx2+1 dy If then equals to : dx O y [2/(x-2)+(3x^2)/(x^3-4)-2x/(3x^2+3)] O…

A: The formulas which are used to solve the above problem are stated with the solution.

Q: dY 1. The system in Section 3.2 - Exercise 1 (previous page): dt Y dt -5 2. The system in Section…

A:

Q: 8x + 4y 14 O non-homogeneous 5x + 7y = 6 O homogeneous 3x 5z homogeneous 3y + 2z Onon-homogeneous -…

A:

Q: 8 Find all the first partial derivatives of z = 5x°y - 8x y. (Choose all applicable answers.) O zy =…

A:

Q: Consider the system of first order differential equations fx'(t) + y(t) = 3e2", x(0) = 1 y(0) = 0…

A: The given question is about the system of differential equations.

Q: 2 4 find the orthogonal trajectories to c¯y y" = 4y´ + x´ 2 2 .... ..... ..... .....

A:

Q: 3 (D2 + 4)y =- Ost<3 3t +2 t23 y(0)=0, y'(0)=1 Find L{y} °L{y} = 1 3. 3e 3s Se-3s 82+4 s(s2+4) s (s²…

A:

Q: Find all the first partial derivatives of z 3a"y-72°y. 5.8 9.6 (Choose all applicable answers.) O 2,…

A:

Q: (2t - 4 0st<2 (D2 – 1)y =- 12 %3D t22 y(0)=0, y'(O)=1 Find L{y} L (y) = F1) 4 2e-2s 2e-2s %3D -…

A:

Q: Fiven the following non-homogeneous system of first-order linear differential quation: у3 2у1 + уг +…

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Q: 5. Given that 8x2 w(x, y, 2) VIVE Use partial derivatives to find the maximum percentage error in w,…

A: Given, w(x,y,z)=8x2y3 z4Percentage error in x, y and z is 1% , 3% and 4% To find: Maximum percentage…

Q: Find all the first partial derivatives of z = 5a y-8y. (Choose all applicable answers.) O z = 40x'y-…

A:

Q: (x + 2)-(x + 2)+y 3x +4 diferansiyel denkleminin genel çözümünü dx2 bulunuz. i riiniiz

A:

Q: Assume Zero initial Conditions * d²y dy +3. + 2y = 0 dt2 dt

A: Solution:

Q: Test 1. y" - y - 2y = e by D- operator method 2. y" - 3y' +2y = ex + 6x3 - 2+ 3sin(4x)

A: 1. Now we will solve the differential equation. The genaral solution: =…

Q: Suppose that a projectile is fired straight upward from the surface of the earth with initial…

A: velocity v = rate of change of displacement y Hence, v = dy/dt Hence, d2y/dt2 = dv/dt = (dv/dy) x…

Q: y" + 4y' + 3y = 0, y(0) = 2, y(0) = -1

A:

Q: Compute the nonhomogeneous linear DE. a. y" -y = x + ex b. y"- 2y + y = x’e*

A: We are given Non homogeneous differential equation. We have to find their solution.

Q: The standard form of 3dy-xydx= 3y³e/3 by Bernoulli's ec 4x/3 dx 3 A dy ху = 3e**/3y3 dx 3 'x=…

A:

Q: Let   dx/dt =   x2y3           dy/dt  = -x - y - (xy4)/2 be a dynamical system.   Is  L(x,y) =…

A: Given function is, dxdt=x2y3dydt=-x-y-xy42......(1) Lx,y=x22+x2y44.....(2) For the proper Lyapunov…

Q: Find all the first partial derivatives of z = 5x°y - 8xy*. (Choose all applicable answers.) O zz =…

A:

Q: 1. 2y" + 3y – 2y = te-2t ; y(0) = 0, y'(0) = %3D 2. dt *+ y = e2t ; y(0) = 0

A: A detailed solution is given below.

Q: What is the general solution to the follwoing equation: (4t+5y+4)dt-dy=0

A:

Q: 3. Find the first partial derivatives with respect to x, y, and z. 6xz 4x+3y dw dw dw 18yz (4x +…

A:

Q: 2t-4 0st<2 (D2 - 1)y = t22 y(0)=0, y'(0)=1 Find L{y} L (1) = 1 + - - 2+ 4 2e 2s 2e-2s %3D | L (y) =…

A:

Q: (3z²+5z+3)dz (z- 2)(z+3) Integrate:

A: The given integral is ∫(3x2+5x+3)(x-2)(x+3)2dx

Q: Minimize F(y, u) = f¿u²(t) dt under ý = -2y + u with y(0) = 1, y(1) = 0. Is your solution unique?

A:

Q: find the first and second derivatives. 1. y = -x2 + 3                                2. y = x2 + x +…

A: 1) Given thaty = -x2 + 3On differentiating y with respect to x,

Q: Draw the slope fields of dy/dt = -t2y at integer values ( y is greater than or equal to -5 and less…

A:

Q: y" + 3y' = 0, y(0) = -2, y'(0) = 3

A: The solution is given as

Q: 2t – 4 0st<2 (D² – 1)y = [2 t 2 y(0)=0, y'(O)=1 Find L{y} O L 1) = + -1) 2e-2s +. s(s² -1) 4 2e s2…

A: To solve given question first we take Laplace transform of both sides and solve.

Q: 2 X u"(x) = −3−2x −²_² +6e² + ½f" (x −1)²u(t)dt, u(0) = 0, u'(0) = 1,u*(0) = 2. - 2

A:

Q: Find the first partial derivatives of the function. W = In(x + 3y + 6z) 1 x + 3y + 6z aw 3 ду х+ Зу…

A: Given :W=ln x+3y+6zTo determine∂w∂x,∂w∂y and ∂w∂z

Q: Compute the partial derivatives. 6x z = V x2 + y2 az 2 V 2x +y dz ду

A:

Q: Find the four second partial derivatives. z = y3 - 9xy2 - 2 a2z %3D a2z дхду -18y %3D a2z дудх -18…

A:

Q: 3- Find the orthogonal trajectories of a system. x²y² – 2xya + a = 0 %3D

A:

Q: x' = -2x +y x(0) = -2 y(0) = 2 %3D y' = -5x + 4y %3D

A:

Q: x' = -2x +y x(0) = -2 y(0) = 2 y' = -5x + 4y %3D

A:

Q: d2x/dt2 + 4 dx/dt + 3x = 2 x(0) = x’(0) = 0

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