The current in an electric circuit is given by the equation di Ri +L==0, dt - %3D where L and R are constants. Show that - Rt i=le L, given that i=I when t=0.

Q: If x? + y2 = 100 and dy/dt = 9, find dx/dt when y = 8. (Enter your answers as a comma-separated…

A:

Q: Given that x and y are functions of time, find the indicated rate of change. dy dx Find when x= 1, y…

A:

Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: Given Volume of cone isV=13πr2hwhere r is radius and h is height and h is constant .

Q: dy Find the value of at t = 1 if dx? Vt2 + t, y = t2 + 3 x = 4

A:

Q: Given y = V4x + 5, find the differential dy when a = 7 and dæ = 0.3. %3| Round your answer to three…

A: Given data:   The expression for the given function is y=(4x+5)1/2. The given value of x is x=7. The…

Q: If x2 + y? = 169 and dy/dt = 5, find dx/dt when y = 12. (Enter your answers as a comma-separated…

A:

Q: Solve J. e-t sint dt. 0,

A: Introduction: The Laplace transformation is very useful in determining the integral. The Laplace…

Q: Find an integrating factor and solve the equation у da + (3гy — e Sу) dy %3D 0. -

A:

Q: The velocity of a particle moving back and forth on a line isy = ds/dt = 6 sin 2t m/sec for all t.…

A:

Q: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

A: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

Q: a - Find h (Stet sinh t sint dt)

A: The objective is to find ∫te-3tsintsinhtdt It is known that, sint=et-e-t2isinht=eit-e-it2…

Q: Give the number of complete oscillations that will occur over 1 minute for a mass- spring system…

A:

Q: t +t dt

A: Antiderivative: Integration is the inverse process of differentiation.  The operation of finding the…

Q: The velocity of a particle moving back and forth on a line is v = ds/dt = 6 sin(2t) m/sec for all t.…

A: Given:

Q: Without integrating, explain why: S, ?)°dx = o x(1+ x* -2

A: To show:     ∫-22x1+x22dx = 0 (without integrating)

Q: Given that S" 4Væ dx = 152, what is fo*4Vt dt ? 3 )

A: As we know that;  the value of definite integral will not change if independent variables changes,…

Q: dz %3D dt

A: Given that: z3=x3+y2, dxdt=2, dydt=1 and z>0.

Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: We have given thatthe radius r and height h of a right circular cone are related to the cone’s…

Q: dy Find for y = /12+13t dt. dv

A:

Q: b) Find fo dy for y = Vt-1 t = sec?x sint

A:

Q: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

A:

Q: The volume V of a right circular cylinder of radius r and height h is V = ar?h. (a) How is 4 related…

A:

Q: + iwe¬lwt = 0. dt = 0,

A: Given differential equation is

Q: e ln (xle) (2– sec²r)cm#/c°sec³x sec(3A – x) What should be the value of A for -dx to be integrable…

A:

Q: Find a solution to the SDE dX; = X,(ydX; + tdt), where y ER is a constant and Xo = 1.

A: The given equation is dXt=XtγdXt+tdt. The given initial condition is X0=1. The integration formula…

Q: The delivery of an antibiotic through an intravenous line (IV) may be modeled by the differential dm…

A:

Q: Find the total differential du. 1. w = y tan a? – 2xy

A: To find the total derivative

Q: The radius r and height h of a right circular cylinder arerelated to the cylinder’s volume V by the…

A:

Q: The rate of change of y is proportional to y. When t = 0, y = 2, and when t = 2, y = 4. What is the…

A: Given that rate of change of y is proportional to y that is, dydt=ky        ...(1)

Q: y = tan o (sin 67E-TT) find dy dt ()

A:

Q: Find the total differential dw. 4. w = e*" – sin(yz) -

A:

Q: The radius r and height h of a right circular cylinder arerelated to the cylinder’s volume V by the…

A:

Q: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

Q: "Differentiate both sides of the equation V = Tr*with respect to t AP (using the chain rule on the…

A:

Q: th² (t) В V = 2

A:

Q: e'dy + (5t + ye')dt = 0.

A:

Q: The work done W,to stretch a spring from its natural length to an extension of 2 meters Is given by…

A:

Q: f 5 J of work are needed to stretch a spring 10 cm beyond equilibrium, how much work is required to…

A:

Q: The velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for all t.…

A: given the velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for…

Q: Find the antiderivative of the given derivative. ds 14(4? – 1)3 dt S =

A:

Q: The radius r and height h of a right circular cylinder arerelated to the cylinder’s volume V by the…

A: The volume of a right circular cylinder is V=πr2h. Consider that neither r not h is constant. Assume…

Q: Find the rate of change of volume at the t= 2 sec If ri=2t-1 hisim hi=3ť-t r2= 3t+1 h2=2m h2=4t-1…

A:

Q: Given y is the square root of x. Find dx/dt when y=2 and dy/dt= 1.75

A:

Q: 60. (a) dx SI dt 1 + √t (b) de fint di dt

A: We can solve this as follows:

Q: The linear approximation at and where B is: = = 0 to sin(9x) is A + Bx where A is:

A:

Q: dt 13. 1 sec t

A:

Q: If x2 + y2 = 100 and dy/dt = 4, find dx/dt when y = 6. (Enter your answers as a comma-separated…

A:

Q: Find the antiderivative of the given derivative. ds = 14t(5t2 – 1)3 dt S=

A:

Q: Find the integrating factor for the equation dy + sin(3x)y 223 dr

A: find the integrating factor

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.