Find dy/dx in Exercises 45–56. dt, x > 0 46. y = Vi + ² dt 45. У sin (1³) dt 48. y = x sin (f²) dt 47. y = dt t² + 4 dt 1² + 4 49. y %3D (t + 1)1º dt 50. y = sin x |xl < = dt 51. y = 2 V1 - 0• dt dt Vi 53. y = 52. У 1 + 12 tanx rsin-'x cos t dt Vi dt 55. y = 54. y = 2* sin-' t dt 56. y =

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

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Q: integrate t2 sin(2t) dt from 0 to 8pi

A: We will  Integrate by parts using the formula:              ∫u v dx = u∫v dx −∫u' (∫v dx) dx.

Q: d²x dx 2 + 10x = e2t x(0) = 0, x'(0) = 1 %3D - dt2 dt

A: Given differential equation is d2xdt2−2dxdt+10x=e2t. and x0=0, x'0=1 Write the auxiliary equation…

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Q: Solve differential equation using Laplace transforms. d²y dy + 4 + 4y = 60 y(0) = y' (0)= 0 dt? dt

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: d²x dx + 2 * + 5x = e-t sin t; dt [ = x(0) = 0 x'(0) = 1 %3D dt2

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Q: 1. 3(3x2 + y²)dx – 2xydy = 0

A: According to our guidelines we can solve only the first question. Please re post the other questions…

Q: Step 3 Rewrite the integration in terms of u and v. 110 Step 4 (cos w)ew dw = (cos w)ew - Again…

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Q: That question please

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

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Q: Compute dy/dx in terms of x and y. 20. Thermodynamics texts use the relationship az %3D ax az…

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Q: = Lasin(t") dt y%3D

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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: find sech Vi tanh Vi dt 49. `csch (In t) coth (n t) dt 50. Vi cln4 •In 2 coth x dx 51. 52. tanh 2x…

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Q: Solve the DE sinx siny dx + cosx cosy dy - O by separation of variables. A sinx cosy - C sin y B cos…

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Q: Find the total differential w = x2yz2 + sin yz

A: Partially differentiate w = x2yz2 + sin yz with respect to x and keep y and z as constants.…

Q: What is the integrating factor of (y – cos² x) dx + cos xdy = 0?

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Q: Let 2x2+ 3x+Y a) Find the differential dy when x = 1 and dx=0.1 %3D b) Find the difiea ial dy when…

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Q: 16 tan- dx 1 + x? dv 19. 20. (1 + v²)(1 + tan¬1 v) Oe® do 2e-0 sin 0 do 21. 22. e tal dx 2хe dx 23.…

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

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Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

Q: -+y= cos 21, y(0)= 5 dt y(0) = 5 %3D

A: Thus solution is

Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. cos y A sin x B sinx cosy =…

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Q: Estimate Ay using differentials. 1/33x-1, y = x ¹/3 e³x-1. a = 1, dx = 0.1

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Q: Estimate Ay using differentials. .1/3 y = x¹/3 e³x-1, a = 1, dx = 0.1 -

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Q: Compute the differential dy for y = 7x° – 4x2. dy =||

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Q: Sketch the direction field of the differential equation y'=cos(xy); trace a solution through the…

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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: Evaluate the deflection of a vibrating string of unit length having fixed ends with initial velocity…

A: Consider the wave equation    ∂^2u∂x2=1c2∂^2u∂t2     .....(1)   here U(x ,t) is the defection of the…

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

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Q: Find dy dt dy dt at x = 3 if y = 5x² + 3 and dx dt 2.

A: Given:-y=5x2+3dxdt=2 at x=3To find : dydt

Q: Is the differential equation (uv+u)du = [(u^2)*(v^2) + u^2 + v^2 + 1]dv separable?

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Q: Can you help me with #11?

A: The given integration is,

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

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Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)V(x) where U(x)and V(x) are…

A: We have to explain of the method of proving the derivative dydx of y= U(x)V(x) where U(x)and V(x)…

Q: Siny dx t sin Zydy + x dy

A: To solve: sin⁡ydx+sin2⁡ydy+xdy=0…

Q: (ye*y)dx + (xe*y + sin(y))dy = 0, y(0) = t exy + cosy – 1 = 0 ЗехУ — сosy — 2 %3D 0 Option 1 Option…

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Q: sin 2ycos 2y cosxdx dx 17. 2. secx+tanx 18. [2sin(3x)cos(5x)dx Vydy 1+y\y 19. [(sin y +2cos y)’dy…

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Q: V4-z2 z siny dx dz dy 16 3. 16 5 0 16 0 66 0 66

A: The objective is to solve the integral ∫0π∫02∫04-z2z siny dx dz dy

Q: b) Find if e Vt2 +5 dt + siny = x- xcosy rsinx ycscx

A: According to Leibniz' rule:

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A: Given Partial differential equation (PDE) ∂u∂y=∂2u∂x2+u Given, Initial conditions u0,y=0 and…

Q: Find the solution. 7. (3siny – 5x)dx + 2x2cotydy = 0 hint: let z = siny

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Q: Can you help me step by step?

A: Given information:

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

A: Given function is y=(1+sin12t)-5

Q: 1. dly dx 2. dy %3D 2X Secy J-(1-xx) oly dx=2y dy dx , Y(1)=0 (Intial Gonditin)

A: There are multiple question. So as per Bartleby policy Kindly ask other question separately. 1.

Q: Find dy/dt of y=(1+lnx)/1-lnx

A: consider the equation

Q: d²x + 16x = 1 + 2 sin 4t dt2 dx (0) = 0 x(0) = 0, %3D dt

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Q: THE IVP

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

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

A: Question is solved.