az Find at (2, -2, 1) if x2 + y? + z2 = 6xz+ 6yz + 21 %3D 8. %3D %3D dy %3D 25 25 1.

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: 9. dy/dt = y²(y² - 1), -∞ < Yo <∞

A:

Q: FIND dy AND dy OF x= VI-t AMD y= t° -st. dx a 4t Vit day dx2 7-1^7- d^y-4t %3D c.)dy – 4t JI-t %3D –…

A:

Q: b) Golve: 4x°y*+4x°4- sx y' + 24= 60x?+8x +1 on Co,00) (2) vsing the Method of Uaniation of…

A:

Q: dy dt (d) di² + 2- 3— 3t + 2, у(0) — У (0) — 0. dy (е) di? dy + 20y %3D —3 sin 2г, у(0) %3 у' (0) —…

A:

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

A:

Q: (xy² + 3y²)dy – 2x dx = 0 is not separable. ylgn ihi

A:

Q: 2. Obtain the particular solution A. yy' 2x(y+ 1) B. (x? + 1) dy = (y² + 1) dx

A: Topic :- Differential Equation

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

A:

Q: 1. If y = V6x + 1, then what is Y? dy? %3D dx dy a. 2(6x – 1) 3(6x + 1)7 2(6x + 1) dy С. dx %3D %3D…

A:

Q: 30 -20 -10 Compare dy with (r-y} dydx 10 20 30

A:

Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: (2y-x)(dy/dx) = 2x + y, given that y = 3 and  when x = 2 Homogeneous equations

A: Solve the following problem by substitution.

Q: dy -y2+1,ysCJse Cantial cokditian.

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: The solution of ë+w?x = fsin wt with initial conditions r(0) = 0 y a(0) = 0 is given by %3D %3D

A:

Q: dy 2. Given: x y = 2x-3y + 2 and- 3D3 %3D dt dx when x = 2 and y = 1 dt Find:

A: Consider the equation.

Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: If y = f(x) is the solution of (5aty – 12a – 2y³)dx + (x³ + 4y³ – 6xy?)dy = 0, f(0) = 0, then

A:

Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1) = 8

A:

Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

A:

Q: Show that if

A: To Determine: show that      dydt=ky1-y Given: we have y=11+be-kt Explanation: we have  y=11+be-kt…

Q: 3. (4r'y-15r-y)dt + (r +3y-1)dy = 0 CS Scanned with CamScarner

A: We can solve this using exact equation of differential equation

Q: dt2 d²y e. ++ 4y = 8t – 10, y(0) = 1, y'(0) = 7 %3D %3D %3D

A: As you post multiple questions According to the guideline I only solve the first problem. Please…

Q: 2 Solue Bor メ= o-5 dx = y X (6) = 0 dt dy =_X yo) =I %3D

A: As per bartebly Guideline we can solve only one question.. Hope you understand

Q: dy If ex+У%3D ху, then dx %3D Ух- 1) A x(у- 1) (1- x) B x(y- 1) x(у- 1) Ух- 1) x(1-у) (D y(x- 1)

A:

Q: 3D In Vi dt y = x/2

A: First of all we will evaluate  ∫lntdt=∫ln(t)12dt=12∫ln(t)dt=12ln(t)∫dt-∫ddx(ln(t))∫1dtdt(used…

Q: 3. Obtain the Particular Solution when x = 4 and y = 1 (x+ y - 4)dx - (3x- y – 4)dy = 0 %3D

A:

Q: y' + 4y = e^(4t) %3D

A:

Q: 2 In(t) and y=4 t2 then find %3D %3D dy dx d'y dx2

A:

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: hich of the following is not variable separable? (А) 2ху dx + (х2 + 1) dy %3D0 A ye' dy - (e-y+…

A:

Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: Let y(x) be the solution of the IVP dy - (y - 3)'dx = 0, y(0)=2. Evaluate y(13).

A:

Q: obtain the family of solutions [x − y arctan (y/x)]dx + x arctan (y/x) dy = 0

A: The detailed solution is given below Thank you

Q: XZ 3) cos(x)-x²y + e + yz = 4, P (0,1,2)

A:

Q: 21. xy' = 3y +x* cos x, y(27) = 0 22. y' = 2xy + 3x² exp(x²), y(0) = 5 = 4x* %3D %3D %3D %3D 23. xy'…

A:

Q: find for x=1 the y value for partivular solutiom, (D^2+3D-10)y=0, when x=0, y=0 and x=2, y =1

A:

Q: The standard form of 3dy- xydx= 3y e* 4x/3 by Bernoulli's equation is: dx = 3e /3,3 ху A dy B y…

A:

Q: 5. y' + 2y = 0, when x = 0, y = 2 %3D Ans. y = 2 e-2x %3D dy 6. xy +2 y– x - 2 ху — Зу+х-3 dx (у -…

A:

Q: () fiz) - y-2xyy ti(-x+ x² y+) + z* そ=メー *y メ eうあ* *y* (-anaty'n g) u cory) +i vexy) 三 wy) = *y*x ;…

A:

Q: -0.08. Then evaluate dy for a=-3 and dz *+1 %3D Let y = dy = %3D

A: We have to find

Q: •ý -2ý +y= ě sinx %3D Ans: y=ě +2xě - ě sinx • ý -uý ruy = 12 /* %3D e 2X 2 ZX .2 +C2 X e + 20

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: 20x -4Dx Dy t40y )u= cos(2X+y)+xy Ans. U= i(y-2x) +x2 (9-2x) + Coslzx+y) +

A:

Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

A:

Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: sec y Then y8 Let z dz dy y16

A:

Q: Obtain the particular solution when x = 1 and y = 1 y(x^3-y^-5)dx-x(x^3+y^5)dy=0

A: Here is the solution of the given differential equation.

Q: dy -2y 3cos3t – 11sin3t dt? dt

A:

Q: 2x? dy 2 - y dr dy = cos z dy x + y dr dy 3x O dy E = y (2 – y) ||

A: The given options are  y'=2x2          (1)y'=2-y         (2)y'=cosx       (3)y'=x+y…