d y. d3y dy d'y dy (+() dy + y dt2" dt + b dt dt2 ay dt3 d/dt (5 %3D dt

Q: 9. dy/dt = y²(y² - 1), -∞ < Yo <∞

A:

Q: dx 8х — 9у dt dy = x + 2y x(0) = 2 y(0) = 1 - dt

A: The solution is given as

Q: .dx/dt = x+y², dy/dt = x + 2y

A: We have to find the critical points of the given system of equations dxdt=x+y2 ,dydt=x+2y

Q: Find an integrating factor for the DE y(4x – 3y – 3)dx +x(x– 2y –- 1) dy=0

A:

Q: Suppose z = x- + y°. Then dz/dt = dx 2- +5 dt dt dx dy +5y dt 2x dt dy dx 10 dt dt dx dy +5y- 2x- dt…

A: Given,                 z = x² + y⁵

Q: d?x ax dx ÷+ 9x = 0, when x(0) = 1 and (0) = 0 dt2 dt dt

A:

Q: х у? dy 1+ y6 ytx dt + t + t3 + (1 – z³)2 ( xy z? dz

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: dx dy - 2x – 2y. a) dt -x, dt dx = x + 3y, dt dy dt 2.x. b) dx dy (c) 3x – 4y, 2x – y. - dt dt

A:

Q: * = x- 2y+ 2z = -2x+y– 2z dt dy dt E = 2x – 2y+ z dt

A:

Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative

Q: If x^2+y^2=36 and dx/dt=9, find dy/dt when y is positive and (a) x=0: dy/dt= (b) x=2: dy/dt=  (c)…

A: Given: x2+y2=36    -1⇒y2=36-x2⇒y=36-x2   -2dxdt=9   -3

Q: dx dy -- x - 2y = 16te', 2x – dt - 2y = 0, x(0) = 4, y(0) = 0 dt

A: We will find out the required solution

Q: 1. -y = dt dy *+ 4x = 1 dt

A: We have to differentiate one of the given equation first to exclude one of the variable.

Q: b- Yt dt + dBt dY; 1-t

A:

Q: d y dy 14. dt2 +2, + y= 2 cos 2t dt У (0) —D у (0) — 0

A:

Q: Solve the following initial value problems using Laplace Transforms:

A: a.) The given initial value problem is,

Q: y = tx2 + tx dy Find dx dy dx + 2tx * dy Find dt dy dt II

A: Given that y=tx2+t4x We have to find dydx  and dydt dydx is the derivative of y with respect to x…

Q: dx dy + y = x , dt = 3y dt dx dy 1.

A:

Q: y? what is dt/dy? 2y +1 if t =

A:

Q: dx If x2 + y2 + z2 = 9, dt dy 6, and dt dz when (x, у, z) %3D (2, 2, 1). dt 3, find %D %3D dz dt II

A:

Q: d²y dy 2 + 2 - y = 0 dt2 dt ك إضافة ملف

A:

Q: Find an integrating factor for the DE y(4x – 3y – 3) dx +x(x- 2y – 1) dy=0_

A:

Q: d?x dy -y = 0, dt? dt dx 2- dt dz +- z = 0, dt dx dy + 3x + dt -4y+ 3z 0; dt dx x(0) = 0, (0) = = 1,…

A:

Q: Find the solution of dy dy +2 - 3y = 2e2", y (0) = 0, y' (0) = 0 dt2 dt

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

Q: dy 2х dx - y = 6e3t, dt dt dy 3x + dt dx - 3y = 6e3t; | dt x(0) = 3, У (0) 3 0.

A: Given, dxdt-2x-dydt-y=6e3t2dxdt-3x+dydt-3y=6e3t, x0=0, y0=0   We use the Laplace transforms…

Q: find dy&gt;dt.…

A: Given function, y=ecos2pt−1

Q: 2y +1 e'y 1+ y? dy dy = t*y dy 4. dt 2. 3. %3D dt dt t

A: See the answer below

Q: d² y dt² + 3 dy dt +2y(t) = 2e²¹ ; y(0)=0_

A:

Q: 6. dy dx + y?x = sin y, dx ay = 7. dt dt 8. Σa (x) dx) d0y = f(x), where d°y = y, dx°

A:

Q: (a) dy/dt = 3y(y – 1) (b) dy/dt = y² – 6y – 7 (c) dy/dt = y cos(y) 1 (d) dy/dt : Y – 2 (e) dy/dt =…

A:

Q: dx 3x – 5y dx = 3x – y + 2z +t-1 dt dt (a) dy = 4x + 8y dt dy (b) 2x -z- 3t2 dt dz x+y+z+t? dt

A:

Q: If y = 3x3 + 2x and dx 5, find dy when x = 2. %3D %3D dt dt dy dt %3D

A: Given, y=3x3+2x  and dxdt=5 We have to find dydt when x=2

Q: (y')² – 3yy' + xy = 0 12 +y = x \dx², S + (S + = 0 dt² dt² dy x*y" + xy" = ex ds t2 \dt², () - t=1 –…

A:

Q: dx + 2x = dt dy + 10 cos t, dt ay + 2y = 4e-2t – dt 业 da if x = dt rstem

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: he given initial-value problem. dx = y - 1 dt %3D dy -6x + 2y dt x(0) = 0, y(0) = 0 0, у (0) %3D 0

A:

Q: d dt dx dy ruations dt - 2x +2y 1-2t, dyx-0. Giv dt 2 dt

A:

Q: dx = -y+y(x² + y² dt dy = x – x(x² + y²) - dt

A:

Q: dx Зх — 2у — z dt - dy 3x – 4y – 3x dt dz - 2x – 4y dt

A:

Q: d²y 5 dy +6y= e7t dt dt2 y (0)=0 y'(0)=2

A:

Q: dx dt dy dt x + 2y -2x – 3y x(0) = 1 y(0) = 2 | |||

A:

Q: d²y dx² -3 dy dt 4y = 3 sin x given y(0) ) = 0 and y'(0) = 0

A:

Q: d'y dy dy -+6 +11-+6y=4 dr dr dt y(0)= y'(0)= y'(0)= 0

A: Given the Ordinary differential equation:

Q: 2,d'y(0) = -2 dt? d'y(t) , dy(t) dy0) - + 3 dt = sec(t), y(0) = 2, dt %3D %3D dt

A: Answer

Q: dy dy + 7 dt + 10y = e-t dt2

A:

Q: 9. dx/dt = −(x − y)(6 — x − y), dy/dt=x(4+y)

A: Given that, dxdt=-x-y6-x-ydydt=x4+y We have to determine all critical points of the system of…

Q: Consider a disease that propagates according to the system dx 3 357 — Зху — Зх dt - dy = X dt х*у —…

A: Given that, dxdt=357-3xy-3xdydt=x2y-13xy-68y The equilibrium points are,…

Q: y") ax Zxy dy 3. x3y dx - (x + y) dy = 0. 2 dy dy LC

A:

Q: dy -2y 3cos3t – 11sin3t dt? dt

A: