If W(f,g)(t) = cost – t sint and if u = f + 3g, v = f – g then W (и, v) (2л) %— - 1

Q: In your words explain what is an integrating factor u(miu) for a linear equation y'+t(t)y=q(t). How…

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Q: The integrating factor of + 2.xy= 5x² is dx dy а. b. x2 e 2 C. 1 d. et

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Q: • The integrating factor of the given DE are already given below. What is the value of "n".…

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Q: What is the integrating factor of the equation (2xy*ev + 2xy³ + y)dx + (x²y+ev – x²y² – 3x)dy = 0 A…

A: We have to choose the correct answer from the given option according to the given condition

Q: The integrating factor of the given DE are already given below. What is the value of "n"…

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Q: What is the integrating factor of the equation (2xy*e" + 2xy³ + y)dx + (x²y*e» – x²y² – 3x)dy = 0

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Q: The integrating factor (IF) of the equation: (2x³y + 4x<y + 2xy² + xy* + 2y)dx + (2y³ + 2x²y + 2x)…

A: Solution: Given: 2x3y2+4x2y+2xy2+xy4+2ydy + 2y3+2x2y+2xdy=0⋯⋯⋯⋯⋯⋯eq.1

Q: 4. Evaluate: S. yx²dx + xzydy + xz?dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

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Q: If xy = 4 and = -5, then what is dt dy when x = 4 and y = 1? dt OA. 8 8. OB. C. 8 OD.

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Q: suppose y = √(3x + 1), where x and y are both functions of t. If dx/dt = 2, find dy/dt when x=5

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Q: What is the rate equation for related to mixture problem? dx = r.c. + r;c; а. dt dx b. = r.C; - r;C.…

A: To find the rate equation related to the mixture problem.

Q: Find the particular solution, Using the integrating factor method: dy + In x =-y where y(1) = 3. dx

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Q: If x =t-1+5 and y 6+t-2 then dy at t = dx is

A: topic - derivatives answer is 4

Q: The integrating factor of dx dy 2 y= 3x² is а. b. 1 x С. d. 1

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Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t² , (0 <t< 1).

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Q: ) L -dx (x² + 1)²(x² + 2x + 2)` sen? t dt, for 0 <b< a. a+b cost

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Q: Use Euler's method to estimate y(0.02) ey-x y' 1 + e²y ,y(0) = 4

A: Given differential equation is y'=ey-x1+e2y with the initial condition  y0=4 and step size is…

Q: • The integrating factor of the given DE are already given below. What is the value of "n" y²dx…

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Q: If g (x): A d dx [e' — In(2t+1)]dt, find g''(x) - -2 4 (2x + 1)² 4 B (2x+1)² Ⓒe*-In(2x+1) 2 D (2x +…

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Q: 39. f(a + 1+2 tag z + tag' x) dx = S (sec" z + 2 tag 2) dz tag z)' dz %3D tag z + 2 In Isec z| + C

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Q: The integrating factor of the given DE are already given below. What is the value of "n" y(y²-x-6)dx…

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Q: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: What is the integrating factor of the linear DE of order one ydx + (3x - 2y +5) dy=0,

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Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: If g(x) = -S^*[e²− ln(2t+1)]dt, find g''(x) . dx 2 (A (2x + 1)2 Be* -In(2x+1) 4 (C) Ce¹+ (2x + 1)² 4…

A: Here is the solution of the given problem.  By using derives under Integral.

Q: 6. If f( x, y) = V x° + 1 y², estimate the value of f( 2.06 , 4.97 ) using the differentials.

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Q: The integrating factor of the given DE are already given below. What is the value of "n"…

A: Given: y6y2-x-1dx+4xdy=0

Q: • The integrating factor of the given DE are already given below. What is the value of "n" y²dx…

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Q: 2e | 3జy S S dy da = Vsin(zy)

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Q: The integrating factor of the non-exact DE: ydx – (x + 6y²)dy = 0 is

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Q: d If g(x) = - S* [e'− ln(2t+1)]dt, find g''(x) dx -2 2 A ex. (2x + 1)² 4 (В B et + (2x + 1)² Ⓒe*…

A: Given that gx=ddx∫-2xet-ln2t+1dt

Q: If x2 + y2 + z² = 9, xp 6, and dy = 9, find dt dz when (x, y, z) = (2, 2, 1). dt dt dz dt

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Q: The integrating factor of the given DE are already given below. What is the value of "n"…

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Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

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Q: t seel dx

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Q: The integrating factor of the given DE are already given below. What is the value of “n” y2dx…

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Q: Given Z = ye¯2a + 3y ; where x = ln 2 and -2x y = 2 with possible errors Ax = 0.01 and Ay errors in…

A: Key points required : The absolute error for the function  fx,y is δf=∂f∂xδx + ∂f∂yδy  The…

Q: Find the integrating factor for ty' + 2y = t5

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Q: The integrating factor of the given DE are already given below. What is the value of "n" yly²-x-8)dx…

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Q: • The integrating factor of the given DE are already given below. What is the value of "n" y²dx…

A: In order to find the value of 'n', follow the following steps.

Q: ex+y+Z If f(x, y) = x+ey+e²> then the %3D ex+eY +eZ > value of fx + fy + fz is equal 2f f

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Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

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Q: Find the particular solution if dy/dt=sin(t) and y(2)=2.

A: Topic:- application of integration

Q: The integrating factor of the given DE are already given below. What is the value of “n” y2dx…

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Q: The integrating factor of the given DE are already given below. What is the value of “n” 3y2dx…

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Q: Admit that for all (x, y), af (х, у) — х dx se (x, y) = 4y ду calculate g' (1) = f(2 cost, sint).

A: We have to prove 4y*f'x - x*f'y = 0 Also calculate g'(t).

Q: (b) If z = 9t²e 4t, find 4 dz dt

A: Given.

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.