dy (a) dt + 2y(t) = x?(t) dy (b) dt + 3ty(t) = tx(t) (c) 3y(t) +2 = x(t) dy (d) + y?(t) = x(t) dt (2) 2 dy +2y(t) = x(t) (e) dt dy dx (f) + (sin t)y(t) dt + 2x(t) %3D dt dy (g) dx +2y(t) = x(t)- dt

Q: of and for the functions: dx dy H.W: Find 1. f(x, y) = (xy-1)² 3. f(x, y) = (x²-1)(y + 2) 2. f(x, y)…

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Q: Let r(t) = Find f(t)dt ( )dt (don't include the +C) fF(t)dt = <[ Calculator 1 Check Answer

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Q: sin(t) dt , 1-4x 1+ t2 4 If f(x) then f' (x) =

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Q: 2 Find dy/ dx: (a) 4y² – 5xy + 4x =10 5х-10 (b) y = 2 x* + 5

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Q: (5) (sec-i x) =, d

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Q: Find the point D'4, symmetric of D4 with respect to the line F4B1. F4: (-2,1,3) D4: (1,2,3) B1:…

A: Here we will find poinr D'4 symmetric of D4

Q: 3 tanx dx 3/ secx

A: Indefinite integral: An integral which does not have any upper limit or lower limit of integration…

Q: (D² +1)y = sec x. %3D

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Q: (16x + 5y)dx + (3x + y)dy = 0 the curve to pass through the point (1,–3) %3D

A: The solution of the problem is given in the next steps.

Q: Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dy…

A: To find the slope of the tangent line to the curve  at the point .

Q: Find dy/dx given xy2 + x²y5 – x³ = 3 %3D -

A: Given that : xy2 + x2 y5 - x3  = 3. Find dy/dx . We know that d(xn)/dx = nxn-1.   Here i attached…

Q: (y² + 1)(x + 1)dy = (y² + 3y)dx → Variable Sep.

A: The solution of a differential equation is defined as the function which satisfies the differential…

Q: dx -y = 5 dt dy = 3t dt 2x -

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Q: (b) sin(y²) dyda 0 X

A: The given integral is

Q: find dy y = sec-1 (e-x)

A: According to the question, we have to find the derivative of the expression y=sec-1e-x. To…

Q: x+y y² +1 #2) (x + tany)dx +- -dy = 0.

A: here we have to solve the differential equation.

Q: dfy = 12 - 30x, y'(0) = 7, and y(0) = 2. dx2 Find the function y(x) satisfying = 12 - 30x, y'(0) =…

A: Given:

Q: x° + x2 + 1 (c) dx. x3 – x2 +2x - 2 arctan x (d) x2

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Q: Find the derivative. tan x y=2x-3 2 dx 蚊ě dy (2x-3)2 dy sec2x - 2tan x (2x-3)2 116 dx (2x-3)sec x…

A: y=tanx2x-3formula used (i)  d dx(xn)=nxn-1(ii)  d dx(tanx)=sec2x(iii)  d dx(ab)=b×d dx(a)-a×d…

Q: (3) Sketch a curve y = f(x) that satisfies: f(0) = 3, and dy dx -2. What is f(x)?

A: The function y=fx that satisfies f0=3, and dydx=-2. We have to find fx and sketch its graph.

Q: d²y + 4y = 8x² ,y(0) = -3,y'(0) = 0 dx2

A: We have to solve the differential equation using initial conditions.

Q: 2y(y2 - x)dy = dx

A: Given data :    2y(y2 - x) dy = dx

Q: (ii) y = e2x cos(1+2x²) (1+2x²)

A: y=e2xcos1+2x21+2x2

Q: find dy/dx if y=((t-1)/(t+1))^2 and x= (1/t^2)-1 at t=2

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Q: Find the value of the derivative dy/dx at  t=2π/3 when an object moves according to the parametric…

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Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

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Q: Pdx + dy = 0, y(-1) = 2. (y 2) dy = 0, y(-1) = 2. ry2

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Q: v (m/sec) 0 A 2 3 4 6 →t (sec) -2/ f(x)dx

A: Solution:Given       for x=5  y=0and x=3     y=2f(x)=5-xTo find∫35f(x)dx=?

Q: y sec t+sec t tan t + (2y+tan t) dt dy xy - (x+2y)2 dx 3y(x' -1)+(x' +8y- 3x) dy -0: y(0)=1 dx

A: Topic:-  differential equations  Note:- as per our guideline if more than one question uploaded than…

Q: (b) 9-(t+1) (42t - sin t)dt

A: Given that the integral is .The objective is to evaluate the given integral.

Q: Find dy dt O A. O B. O C. O D. 2 for y=(5t²-4t) ². dy dt dy dt dy dt dy dt = 2(10t-4) = 2 (5t² - 4t)…

A: Given: y=5t2-4t2We need to find dydt.

Q: d²y + 49 + 4y = 0, y(0) = 3, dy (0) = 1 %3D %3D %3D dx2 dx dx

A: Given differential equation is second order, homogeneous linear differential equation with constant…

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A: Intigrating the given equation.

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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.