dy + y = ť°, dt

Q: Find dx | cos (P) dt y = dx I3D

A: NOTE: Refresh your page if you can't see any equations. . use the integration rule

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: dy sin(y + t) dt %3D

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Q: find dy/dx

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Q: N3xy -y,whtre x sint and y =e. find dwl dt whin

A: w=x2y-y2x=sin ty=et

Q: I=Jx Incx) dx, where b is a constant with %3D bフ)

A: Intregation of product of two variables is given below

Q: Rewrite dx d?y + 3 +y: Sin t ニ dt? dt? dx -4X +S = Cost dz? dt

A: the approach follow:

Q: da at I = –1if y = – 1² + 2 and dt dy dt 2. Find da dt

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Q: Find the general solution for y(t) where, dy 10t dt y II

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Q: Find the solution of y' + y = , sin(t – t)y(t)dt, y(0) = 1

A: using  laplace transform we can solve the given problem using following formulas ; Ly=YLy'=sY-y0and…

Q: dy dx Given y=x³ - 2× and = 3. Determine the value of dt when X=2. dt

A: Differentiate the equation y=x3-2x with respect to t. y=x3-2xdydt=3x2dxdt-2dxdt=3x2-2dxdt

Q: d²i di 1 d. +R- +-i= E@cos ot dt? dt C a'v a'v ôy = 0 е. ôx

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Q: (1) y'(t) = 1- sint – , y(t)dt, y(0) = 0 %3D

A: As per guidelines, we will solve only first question. Kindly repost other question separately.

Q: utt = 0; x € (-0o; c0), t E [0, o) equation for u(x,0) = at

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Q: dy cos(r + y) y(0) = %3D %3D dx

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Q: dx dy 5et %3D dt dt

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Q: dy Find dx, y= [v1+ ť dt

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Q: |e*y dx+e* dy; C: r(t) = (t+ 1, ),-1si<3 Exercise 97.

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Q: Find dy/dx

A: Given:y=∫0ex2 1t dtIntegrating formula∫xn dx=xn+1n+1

Q: (e) dy if y = (t +1)(t + 9) %3D dt It%3D3

A: Given that y=(t2+1)(t+9)

Q: y = f VI + t? dt Y : 0. t2 dt

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Q: cos t dt t10 y = dy dz

A: Known fact: ddx∫pxqx ft dt=fqx q'x-fpx p'x.

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

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Q: Calculate dy/dx at the point indicated. c(t) = (e^t − 1,sin t), t = 20

A: Given: ct=et-1,sint t=20

Q: dy Find -given that dt dx x2 + y? = 2x + 4y, x = 3 y = 1, and 7 dt dy dt

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Q: dy =r-ky, y(0) = y, dt

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Q: dx dy %3D 2x + 2) + 1 dr dt dx +2 dt J+ 3 dt

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Q: dx dy = r°y – ry dt = y - ๕ dt

A: We will answer the first question since we only answer one question at a time. please resubmit the…

Q: d’y ,dy -2+5y = e" cos 2x b) t dt dt

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Q: Find dy/dx

A: To find the derivative of y=∫x0sint2dt. We know that, ddx∫xafxdx=-fx Therefore,…

Q: dy Find dt y = tan? ( sin 't) dy dt

A: Topic :- Derivative

Q: dy Find dt y = (t sin t)6 dy dt

A: Given: y=t sin (t)6 We have to find dydt: Consider, y=t sin(t)6=t6 sin6(t) To find dydt…

Q: dx dt +y = et dy dt

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Q: d²y dt² d'y 11. + (cos t)- dt4 +y=e=tsin t

A: Given - d4ydt4+(cost)d2ydt2+y=e-tsint To determine whether the given differential equation is…

Q: dy y? y(to) = 0 2t dt

A: Given                  dydt=-y22t,     yt0=0

Q: dx = t(1+ t?) sec? x dt

A: Given, Given equation is seprable

Q: dy Find dx T/4 | cos ()dt y% = CoS X, dy %3D dx

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Q: d t sec(t) dt dx

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Q: y=√x Find dy/dt, given x = 4 and dx/dt = 3 Find dx/dt, given x = 49 and dy/dt = 8

A: We have to find dydt given x = 4 and dxdt= 3 Find dxdt, given x = 49 and dydt = 8

Q: dy %3D dx sec? x sec y

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Q: Find fa and fy. f(x, y) = 4e dt %3D

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Q: Find dy/dx. - tsin(t), y = t² + 5t %3D %3D

A: givenx=tsinty=t2+5tfirst we differentiate these two then we evaluate dydtdxdt which is equal to dydx

Q: dy Find dt y = cot? (cos t) dy dt II

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Q: 37 Y= Sin (t?)dt o dy=?

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Q: dy when Find dx x(t) = te', y(t) = 2t + e'. %3D

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Q: find dy/dt. y = sec2 πt

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Q: Find dy/dx

A: Differentiation: y=x∫2x2 sin(t3) dtdydx=ddx[x∫sin(t3)dt]

Q: J cos Vx dx X,

A: =?

Q: y sin (r²) dt

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Q: Find dy/dt. y = cos(~/4t + 11) %3D

A: The given equation is, y=cos4t+11 So, the derivative of the given function is:…

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.