x' = -y – x(x² + y2)² y' = x – y(x2 + y2)², x(0) = (6, 0) %3D %3D

Q: x² – 16- vx2 – 16 8ln (x + %3D 112

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Q: solve. (exy + e²) dx + (zey + e*) dy + (ey −exy - e'z) dz

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Q: Differentiate. y= In [(x +2)° (x + 5 (x+ 7)°] [In [x+ 2)° (x +5)*(x + 7) ]] =O dx

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Q: Solve for y: O y = Oy = x = 4ln(y - 8). 1 4 ln(x - 8) x+8 4 O y = e-4x + 8 O y = 4 ln(x - 8) Oy =…

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Q: f(x) = 1– 2x – x2

A: Nothing is clearly mentioned here so i am solving it by considering that you want to differentiate…

Q: B. Use Set Notation to Describe the Figure U 1. A B 2. A 5. U A U U 3. 4.

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Q: y=3x+4 / 2x+1 y`(0)=?

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Q: Integrate S(x-4)(x²-8x+12} dx

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Q: 3. dx (x²+1)² -3 d x XVX +3, dx x2

A: Evaluate the given integrals

Q: y-y1=m(x-x1) y-(-1)=4/5(x-(-1)) y+1 = 4/5x + 4/5 y=

A: The given equation is y+1 = 4/5x+4/5      y = 4/5x+4/5-1         = 4/5x-1/5

Q: 2 (x-4) dx = (S %3D 2.

A: Given : The definite integral is ∫02 ( x - 4 )2 dx .

Q: Solve: (xy – 1) dx + (x² - xy) dy = 0 %D |

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Q: V3/2 1 dx%3D 6). V1- x 1/2

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Q: y' = x - 4xy

A: We have to find solution of differential equation.

Q: +8x-x +2x +1 (x² + 3)(x' +1)

A: SImplification of the given function helps to find the required integrated function. The partial…

Q: x - 3x-1 dx x'+x-2x 6. Evaluate A. In- C. In -C

A: Given integration is: ∫x2-3x-1x3+x2-2xdx  To find the value of integration.

Q: n/3 sec23x 8. n/4 2+4tan 3x dx

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Q: 3x+4x+1 6. J x-x+4x-4

A: Indefinite integration

Q: c. g(x) = (10 – 2V)(3lnx + x³) Answer: g'(x) = , Sinx d. y = 6+0.5x2 (do NOT expand) Answer:

A: Derivative of given function

Q: Find dy when x=3 and dx = 0.2. y=x-5x³ +3x² + 2x-7

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Q: Solve the nonhomogeneous equation using the method of undetermined coefficients: y" – 2y' – 3y = 4x…

A: First we will find the complementary solution using the roots of the auxiliary equation then using…

Q: Solve (yz + хуz) dx + (zx + хуz) dy + (ху + хуz) dz =

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Q: 2x+(4x+y-6)dy/dx=y ODE

A: In this question, we need to solve the given ODE.

Q: -1)/(x4))1/2

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Q: x^2(lnx-lny)dy=y(ylny-ylnx)dx

A: Explained below

Q: ), y(0) = 4.6, y'(0) = - %3D

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Q: y' = e2x + y – 1

A: Using method of linear differential equation.

Q: (2xe + e*)dx + (x² + 1)e'dy = 0

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Q: 41Stañdx= Q22x+1 X'+2X+1

A: (1) Given integral is ∫tan−1xdx It can be written as ∫tan−1x⋅1dx Use integration formula…

Q: y=1/4x+17/4 ;    (1,4), (5,3) How do I find the net change?

A: The given linear equation is y=-14x+174. The given points are (1,4) and (5,3).  We have to find the…

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.