ds k(4nr). dt --Select-- %3D volume dV k dt surface are ds - ). dt dV dt dV = k(4tr²). dt

Q: Calculate the total differential dz for z = r sinh(ry) + yelv

A: Note- since you have asked multiple questions, So Acc. to Bartleby guidelines we are supposed to do…

Q: dy If y = (t + 6t + 4) (3t2 + 4), find dt dy %3D dt

A: it is required to find the derivative.

Q: 2x + 7x +3. If Ax = 0.3 at x = 4, use linear Let y approximation to estimate Ay %3D %3D %3D Ay =

A: Given y=2x2+7x+3 if ∆x=0.3 at x=4 we have to approximate ∆y using linear approximation.

Q: Find the external in the isoperimetric problem of the extremum of subject to f(y² +xy'- :“)dx= 2,y…

A: Consider the functional  Iyx=∫x1x2Fx,y,y'dxwith the conditions yx1=y1 , yx2=y2and Iyx=∫x1x2Gx,y,y'dx…

Q: find a general sulution to the differential eguatiun using variation of A parametert b)yィyニ tantee…

A: Method of Variation of Parameters: This method is quite general and applies to equations of the form…

Q: Calculate (x²+y²) dx dy area when D is the limited to x²-y²=1, x²-y²= 9, xy = 2, xy=4

A: As per the question we are given a double integral over the 2d region D bounded by the following…

Q: 20 dv on the interval [0, 20] dt du dt 20

A:

Q: Sketch the region of integration. 1. dx dy 1 +>

A:

Q: V24z – 2z3 dz dy dæ, by changing the order of integration to dæ dy dz.

A:

Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: dz Z 1. around unit circle of radius 1 and center at (0, 0) counterclockwise. 2. By using direct…

A:

Q: Sev dx (Hint: Integrate by parts with u-substitution)

A: To evaluate I=∫exdx

Q: Find y(2) and yG) For fundion yft) that saticFies initial-valve dy +2 dy +y dt =2+ (t-3) 6 Ult-3) ;…

A:

Q: 3. Linear DE of Order one 2y(у? — х)dy %3D dx

A: Linear equation of dx/dy form is made

Q: dv Integrate ду 1 partially with respect to y. II

A: To partially integrate the given function with respect to y, implies x will be treated as a constant

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: Find dy/dt of y = Ssin (cost) and simpli -t -cos t cos t V1-? the

A: Given:- y=sin(cos-1(t))  To find:- y'

Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: Evaluate the line integral curve C: x = = 4 cost, y (5x + 7y)dx + (3x − 6y)dy along the = 8 sint (0…

A:

Q: 2. y(2x – y + 1)dx – x(3x – 4y + 3)dy = 0

A:

Q: Evaluate the integral / (10x + 15y)dx + (18x – y)dy along the paraboli - arc y = x² from (0,0) to…

A:

Q: Evaluate double integral.

A: Let the given equation is ₀∫⁴₀∫⁴x  (√(xy)) /2  dxdy The double integral formula is a ∫b c∫d f(x,y)…

Q: Sketch the region of integration. "In 10 r10 1 dy dx In y

A: As y varies from y = ex to y = 10 , we see that x varies from x = 0 to x = ln 10

Q: raluate the double integral : (x + 2y – 2) dy da

A:

Q: dy at x = dt dx Find - 4 if y = 4x² +1 and -2. %3D dt dy %3D dt

A: Take the derivative with respect to t and put the given values.

Q: Evaluate 9 + y² dy dx by first interchanging the order of integration. Sketch the region of…

A:

Q: Evaluate the double integral. y dy dx

A:

Q: dy Find for y = cos (8at + 1). dt dy dt

A: We have to find out dy/dt for given y

Q: Find the total differential. z = 10x6y7 dz = %3D

A:

Q: dy at z = 5 if y = 5x² + 4 and dt dz Find 3. dt dy dt

A: Given y=5x2+4 -1and dxdt=3

Q: The integrating factor of the linear DE dy + ycot x = sin x dr

A: Given: dydx+ycotx=sinx

Q: Evaluate the double integral. (x - y) dy dx (x + y)3

A: To compute the double integral, ∬f(x,y)dydx, first integrate the function with respect y, while…

Q: Evaluate the line integral. -y dx + x dy segment from (3, 0) to (0, 3) x2 + y2

A: Find the slope of the line through the given points.

Q: Find the total differential of  w=x3yz+xy+z+3

A:

Q: Vy+I ydx dy -1 -Vy+1

A: Let's find.

Q: +5y )dx+(2x-4y) dy edary of the region lying between

A:

Q: Find the total differential. z = 5x³y4 dz =

A: Solve the given

Q: Evaluate the integral (4x +9y)dx + (9x – y)dy along the parabolic arc y = r from (0,0) to (1,1). (4x…

A:

Q: . Use fourth order Runga Kutta Method to find y at x=0.1, given that dy = 3e* + 2y , y(0) = 0 and h…

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Q: dz + et+z = 0 dt

A:

Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

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Q: Find the partial integral. Y dy

A:

Q: a) dz, T: z (t) = -e-int, 0<t <1. %3D -1 1

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: What is the integrating factor of (ry + y) dr + (r + 2y-1) dy %3D

A: Given xy+y2dx+(x+2y-1)dy=0Compare above differential equation with…

Q: Find the total differential. z = 6x *y5 iz

A:

Q: Can you help me step by step?

A: The given function is

Q: ds Find where Vt +s = 2s . %3D dt

A:

Q: Sketch the region of integration. sin x dx dy 1.5 y. 0.5 y 3 -05 21 -1 -1.5 1- -1 1 3. 4. 4 0.5 2.…

A:

Q: Ssinx Losxdx X. a) vse u=coS X Esie to evalvale %3D b) Vre V=Sinx to e valvate %3D

A:

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.