Consider the (DE): (12 + 5xy)d + 6x + 3x dy = 0 %3D (a) Verify that u = x°y? is an integrating factor for the (DE) (b) Solve for y the non-exact (DE)

Q: (b) J 32+3 22²-2-1 dx

A:

Q: dx 2x² + 5x +1

A: The formula for the integration is given by  ∫dtt2-a2=12alnt-at+a+C.

Q: Use the Chain Rule to find dw/dt. w - In (√x² + y² + z²), W = dw dt - Need Help? Read It x = 6…

A: See the details solution in below

Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t= 0

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Q: x(3-5x) 2. dx (3x- 1)(x – 1)²

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Q: In question (c), please use the computed result to explain why Dx=c is inconsistent

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Q: Evaluate: IIncx + y) – dy dx 3 a² \In(2a) – –In(a) – + Ei(-a) – In(a) – In 2 +- Ei(-1) А. B. a*…

A: We are asked to evaluate the double integral:…

Q: Find the linearization of the function a) z = cos(sin y – x); at (-2,0) and use it to approximate…

A: Suppose f(x,y) be a differentiable function at (a,b). Then linearization of f(x,y) at (a,b) is given…

Q: 3. Integrate the following: 2x+3 i. J7+3x ii. S V1- cos x dx iii. S cos3 x dx

A:

Q: dx (2х — 5)10 Integrate -

A: We have to solve the given integral : ∫x(2x-5)10 dx = ?

Q: S(1- cos )´sin ź dt, u = 1 – cos 4. U = V5x+8' dx ,u 5x + 8

A:

Q: 2- The homogenous diff. equation can be put in the following form: B- y' f(x)

A: Here we will find the correct option,

Q: Use the method of Characteristic to solve U t tuux = 2t, u(x, 0) = 3x.

A:

Q: b) Evaluate the value of I = S(eºy − 3x) dx + (6xey + y)dy, where C' is the parabola y = C (0, 0) to…

A: The integrand is given here as         (e6y - 3x)dx + (6xe6y + y)dy        = (e6ydx + 6xe6ydy) -…

Q: Which of the following is not linear ? y" xy" + 3 = T y" + 3y' + 2u = (sin 7) 2'y" + ry' + 4y = e…

A: We will solve the problem

Q: Show that y1(t) = cos(3t) and y2(t) = sin(3t) are linearly independent for all t

A:

Q: Amour 1 y (2xy +1)dx +x (1+2xy –x'y)dy =0 It represents the integration factor of the equation

A: If the equation fx,yy dx + g(x,y)x dy =0 is not exact i.e,∂M∂y≠∂N∂x ,then the integrating factor of…

Q: x ln xdy + (y-2 lnx)dy = 0

A: Given: The differential equation xlnxdy+y-2lnxdx=0 Find the integrating factor for the given…

Q: d. Evaluate dx dt (t2 +2t) -1

A: We use the Leibnitz rule of differentiation under integral sign to solve the given problem.

Q: The functions cos r and cos- are linearly dependent (0, ) on

A: evident from the two curves that after zero in a positive direction the two graphs coincide with…

Q: Determine the integrating factor of z = 2xy – x %3D -2x 2e 2 2x e Option 3 O Option 1 None of the…

A:

Q: dx V(z – 2)° – 11 Vxt-2)* - || x - 2 du 1 (steps) da = /11 du: V1I u = x-2 du = dx Substitute u =…

A:

Q: make use od auxiliary questions to solve (y²+yz+z²)dx + (z²+zx+x²)dy+(x²+xy+y²)dz=0

A:

Q: dt 4е-t — et

A: ∫14e-t-etdt=∫14et-etdt=∫et4-e2tdtlet  et=uthen∫et4-e2tdt=∫14-u2du

Q: I = 1- 6x?y dx dy.

A: In double integration, we start integrating from the inner part with respect to the inner variable.…

Q: y? – a? -, y(1) = -V2 dx dy xy

A:

Q: Determine the volume produced by the region bordered by x² - 4x - 4y + 4 = 0 and y = 1 about the…

A: We will use disk method to find volume of solid generated

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.