Q2/ by using chain Rule to find dw at t = 1 if dt w = 2ye* – Inz ,x = In(t? + 1), y = tan 1t,z = et

Q: Show that the 2-D Heat Equation dx² ди becomes ди if x = es cos w and y = es sin w. You ma dt dy?…

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Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

Q: 1. Suppose y = f(x) and that x is changing over time. How is dy/dt related to dx/dt?

A: Given that: y=f(x)

Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

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Q: dx dy Find at x = 1 if y = – 5x´ – 3 and 5. - dt dt dx dt

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Q: If x2 + y2 = 25 and dx/dt = -2, then what is dy/dt when x = 3and y = -4?

A: Given x2+y2=25Differentiating with respect to t,ddtx2+y2=ddt25

Q: Which of these gives an integrating factor for dy 2ty = 3t + 1 dt -

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Q: Compute the differential dy for y = (2x + sin x)². dy =

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Q: If x^2 + y^2 = 25 and dx/dt = -2, then what is dy/dt when x =3 and y = -4

A: Given that  x2 + y2 = 25   .... (1) dx/dt = - 2 To find dy/dt when x =3, y = - 4

Q: Find the differential dz of the function f(z, y) = 4g²+z*y – 2xy and use it to approximate Az at…

A: Consider the given information:

Q: 2. Using Euler's method with N = 8 and 10. dx/dt = 1 + tsin(tx), x(0) = 0

A: Given dxdt=1+tsintx  and x(0)=0 and N=8, N=10

Q: If xy^2 = 4 and dx/dt = -5, then what is dy/dt when x = 4 and y = 1?

A: To find dydt, when x =4 and y =1. Given information: xy2=4 and dxdt=-5 Formula used: 1.)…

Q: dz Use the chain rule to find Ət z = tan (x – 8y), x = s cost, y = e² •Int Se dz 1+(x²– $y}² dt dz -…

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Q: tany = C secx

A: The question clearly asks us to find the family of orthogonal trajectories of the given family.…

Q: 1. Find the total differential of the ff. at (1, -2).

A: The given function is f(x,y)=xy2-3y+2

Q: Q6. Using Rule l-IV to find an integrating factors. (x² + y² + x)dx + xydy = 0.

A: Given- x2+y2+xdx+xydy=0 To Find- The integrating factor of the above differential equation.

Q: By using Laplace transform to solve y" + y = e with y (0) y (0) = y" (0) = 0, what would be Laplace…

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Q: dy Find at x = dt – 4 if y = dx - 2x2 + 3 and dt 2. - - dy dt ||

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Q: dy 2. sec²y secx dx ;y(0)=0

A: The given differential equation is dysec2y=dxsecx and y(0)=0

Q: ) Find: dx/dt  at  x=−4  if  y=−3x^2−2  and dy/dt=1. dx/dt=

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Q: d²x dx + sinx=0 +2. dt for small excursion about x = T/4. 1. Linearize dt

A: d2xdt2+2dxdt+sin x = 0 - (i)here, the above given equation is homogeneous (RHS=0) but non-lineardue…

Q: Find the differential dy of the glven function. (Use "dx" for dx.) 7 y = 3Vx + dy =

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Q: Suppose that a body moves through a resisting medium with resistance proportional to its velocity v,…

A: (a)

Q: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

A: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

Q: 4. Given xy+x*y=2 such that d/dt =2 in/sec. Find dy/dt for x= 1

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Q: Find the differential dz of the function f(x, y) = 4y² + x²y-2xy and use it to approximate Az at…

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Q: Compute the differential dz of the function. z = x*y" ,7,,11 dz

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Q: Find the solutton of followins ordinery differential e quation. yl- 2y' +y

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Q: dy Find at x = dt dx - 1 if y = 2x? – 3 and dt - 2. dy dt ||

A: y = 2x2 - 3dxdt = -2dydt = ?   at x=-1

Q: 2. Use the 4th-order Runge-Kutta method to integrate dx = t - sinx dt given x(0) = 1, using a step…

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Q: 5) If y = x³ + 2.x and dx/dt = 5, find dy/dt when x = 2.

A: Q.5) If y=x3+2x and dxdt=5 Find: dydt when x=2

Q: The integrating factor of Linear differential dy equations + y × 4 tan x = sec²x is dx . O tan 4x O…

A: To find the integrating factor for the below linear differential equation. dydx+y×4tanx=sec2x

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

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Q: Aparticle moves on the graph of y^2=x+1 so that dx/dt=4x+4 what is dy/dt whrn x=8?

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Q: Create a slope field of the differential equation dy cos(t) + cos(y) dt and draw solutions…

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Q: The time rate of change of liquid circulating in two tanks is govemed by dy -0.02x + 0.02y, = 0.02x…

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Q: 5. dx/dt = (4+x)(y-x), dy/dt = (10-x)(y + x)

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Q: Give the integrating factor for 3((y^4)+1)dx+4x(y^3)dy=0. (in terms of x)

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Q: Suppose 4x + 9y - 25, where x and y are functions of t. (a) If dy/dt-, find dx/dt when x = 2 and y =…

A: Given: 4x2+9y2=25 Since, x and y are functions of t, therefore differentiating each sides with…

Q: Find dy dy dt at x = z - 1 if y = -5x² + 3 and dx dt 5.

A: topic:- derivatives

Q: dt What is the linearization of h(x)= 6+ at x=1? cos (1 -1)

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Q: Create a slope field of the differential equation dy = cos(t) + cos(y) dt and draw solutions…

A: Given: dydt=cos(t)+cos(y) To find: Slope field To sketch: The solutions corresponding to y(0)=0.5,…

Q: Q10.a) Find rsinx if tnx Jt +5 dt + siny = x – x²cosy

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Q: If x3 + y3 = 9 and dx/dt = -3, then what is dy/dt when x = 1 and y = 2?

A: Given,

Q: Find dy/dt Y=(1+Sin 12t)^-5

A: Given function is y=(1+sin12t)-5

Q: THE IVP

A: Consider the provided differential equation with initial condition is,

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

A: Topic = Derivative As per guidelines , at a time only one question can be answered. pleas repost for…

Q: What is the integrating factor of 2ydx + x (x² ln y – 1) dy = 0 ? Oy O y?

A: Question is solved.

Q: Can i get help step by step please

A: