11 FCF)dt= fCx) dx =- 43 then 1.

Q: 9. dy/dt = y²(y² - 1), -∞ < Yo <∞

A:

Q: dy sec (re ), y(In 4) = 3 / t dt

A:

Q: 8. Integrate by parts: a) St csc? t dt b) S x2 In x dx

A:

Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

A:

Q: dy satisfies dx? 2 iven by

A:

Q: EVALUATE AND SOLVE THE LINEAR DE. d²x dx + 2,+ 5x = 8e¬ dt2 dt dx When t=0,x=0 dt 8 =

A: Given that: d2xdt2+2dxdt+5x=8e-t

Q: Evaluate 3xz dV where E = {(x, y, z) | 1 < æ < 3, x < y < 2æ, 0 < z < x + 3y}

A: ∬∫Ef(x,y,z) dV = ∫x=ex=f∫y=cy=d∫z=az=b f(x,y,z)dzdydx                                where , E…

Q: 5. f'(x) dx = Choose... 6. cosh t dt = Choose...

A:

Q: Show for Re(z) > 1 dx = r(2) ((2). et - 1

A:

Q: Find dx/dt given that 4x^2+9y^2=13x  x=1,  y=-1 and dy/dt = 10

A:

Q: dt z = cos(x + 4y), x = 5 t ³, y = 8/t

A: We need to find out the value of dzdt

Q: (dx — Зх — 2у dt dy 3D —х + 3у — 2z dt dz = -y + 3z dt %D (λ1, λ = 3, λ5)

A:

Q: d?z dz +3- 2z = te-2t dt z(0) = 0 ; z'(0) = -2 dt2

A: Given differential equation is, 2 z'' + 3z' - 2z = te-2t z(0) = 0; z'(0) = -2

Q: x°y" + 2x?y"+ xy'-y=0

A: A homogenous linear differential equation with variable coefficients given by,…

Q: When choosing u and dv, we want a u that will become simpler (or at least no more complicated) when…

A: The statement is regarding the formula for integration by parts.

Q: Provide an appropriate response. If xy + x = 12 and dx/dt = -3, then what is dy/dt when x = 2 and y…

A: We will find the value of dy/dt with the help of the given data x=2 ,y=5 and dX/dt=-3 as following.

Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

A:

Q: 1 dy J yi + 3y² + 1

A:

Q: (a) Let I = dx. Show that I² = dx dy. R2

A: Note: "Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Reverse order, then integrate SaE ) dydx. Vx \1+

A:

Q: (6xy)dx + 4y +9x ² )civ = 0

A:

Q: QS A) Find IF y = - Ve IF y =-Vt and t sinx

A:

Q: when (x, y, z) = (2, 2, 1). dt dz dy If x2 + y2 + z2 = 9, dx 8, and dt 4, find dt %3D %3D %3D dz dt

A: differentiate the given function with respect to 't' 2x dx/dt +2y dy/dt +2z dz/dt =0 Now substitute…

Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: 一3十 Sin zt dt

A: We have to use first shifting property and Laplace transform of integration property to Laplace…

Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: dy 3) Determine the of : In (ху?) %3D х у dx

A:

Q: dz Find dt if z = x²y – sin y, x = vt? +1 and y = e -

A:

Q: To integrate x3 exdx, we apply integration by parts and in the form u dv, dv is set as: O ex dx O…

A: We have to find the dv

Q: 2f sen jz įdz -2 cos z + C 28. sen Jz dz = %3D

A:

Q: Vēt VE dt

A: Our Aim is to evaluate the integral given below:-

Q: Find dv ifv = t- dt

A:

Q: (b) Calculate e cos(Tx) dx using integration by parts as many times as necessary.

A: Given: ∫excos(πx) dx The formula for integration by parts is given as…

Q: If x'+y' +z-9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x,y,z) (2,2,1)

A:

Q: dz + et+z = 0 dt

A:

Q: b.Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x,…

A: Given that, v=yxy=vx

Q: 2. u(x)= secx+à So u(1)dt.

A:

Q: If y = x2 and dx/dt = 3, then what is dy/dt when x = -1?

A: Differentiate both sides with respect to t.

Q: sech 2t dt Evaluate 3, coth 2t

A:

Q: dy 38. dt у сost

A: Given Information: The differential equation is dydt=ycost. Calculation: Calculate the general…

Q: dx dy If L = Va? + y?, = -5, and dt = 2, find dt dL when a = 3 and y = 7. dt %3D dL dt

A: Given query is the derivative of L over t at x = 3 and y = 7.

Q: Solve for x = u + 1 and y = 2u² - 4u d²y dx² with respect to the parameter u

A:

Q: 1. Evaluate a dV where E = {(x, y, 2) E R³ | 0 < z < x + y,0<x < y?,0 < y< 1}.

A:

Q: Find, if y (3 z)t* + cosec (t) + Z In(2t + 3) dt2

A: First of all, let's get rid of Z by substituting Z = 43 in the equation above: y = (3 x 43)t4 +…

Q: S 6 ttan t dt = %3D dx Jx

A:

Q: zp dt

A: we have to solve the differential equation. dzdt+2et+z=0

Q: dy -2y 3cos3t – 11sin3t dt? dt

A:

Q: Can i get help step by step please

A:

Q: If you have the equation dx/dt = a,are you allowed to multiply both sides by dt to change the…

A: We have given,

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.