The homogenous D. E. with constant coefficient of at least order which has the solution y = 2x? + 3e* + ecosx is O p6) 12y" = 0 5y(5) + 9y(4) + %3D + 3y(5) + 4y(4) + 2y" = 0 %3D y(6) 4y(5) + 9y(4) + 5y" = 0 %3D (9) O 5y5) + 7y(4) + 5y" = 0 5y(5) 10y" = 0 + 9y(4) +

Q: Find curl (3z i + 4x j + 9y k). curl (3z i + 4x j + 9y k) = ( i )i + ( i

A:

Q: 9) =tx-9i Find g8a-16 x-9,Find g9 -16) %3D -16) sa-16

A: Given,

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A: To evaluate the following integral.

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A: Given query is to find indicated angle.

Q: Q/IF it was AY ₁2) = -12 Y(2) ℗ Y³ (2) = − 12 ⒸY² (2) = -11 Y³ (2) = -11 DÝ (2) = -13 © ²³ (2) = -13…

A: Given

Q: 3. Discuss how to transform the graph of y = x2 in order to obtain the graphs of #2a and #2b above.…

A: 3(a):

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A: Given that 4x2-9y2=1 Find the third derivative

Q: If fCx)=4x+ Ax²+ 6X-3 andf(2) =1 what is the value of A? %3D %3D

A:

Q: 1. The quadratic function y = x+ 2x-1 is expressed in vertex form y = a(x-h)2+k? a. y=(x+1): + 1 b.…

A: 1.b 2.c 3.b

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A:

Q: Given g(x) = 6x – 15x +4x +8x–4 and )= 3x² – 3x – 1, what is the quotient ? A 2x – 17x+10 A 2x-5 B.…

A:

Q: 2. x + y – z = 2   2x + 2y - 2z = ­6  5x + y – 3z = 8

A:

Q: - 25. 16: Substitution Method ( 2a3 + 3z dx x4 + 2x2

A: To find the integration of followingI =∫2x3+3xx4+2x2dx

Q: Let (-1,(-1) = 2), (0, ƒ(0) = 5) and (1, f(1) = 6). Which one gives quadratic spline functions?…

A: Given, -1,f(-1)=2,(0,f(0)=5) and 1,f(1)=6

Q: Let f(2) = x² +1 and g(z) = z² - 1 Then (fo f)(z) -X (fo g)(x) (go )(x) : x*4-x^2+1 x*4+x^2-1 Note:…

A: Consider the following functions: fx=x2+1gx=x2-1 ffx=x2+12+1=x4+2x2+1+1=x4+2x2+2…

Q: 2. Find the equation f(x) = ax + b of the least square line for the points (1,0), (-1,2), (2, 1).

A:

Q: 6. (t -1)+(2 8. (2x² +5xy+ 3y²)+(8x² –7y²)

A: 6.

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A:

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A:

Q: 1. Given the algebraic function x² xy + y² = 3

A:

Q: x2 + 4y? – xy + 6x – 5y + 1. -

A:

Q: 4. у + 2x &y(1) = 2. y3

A:

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Q: (D³ – D)y = 4e * + 3e2x X. a. Ур а. у, — 2хе * + 2xe+ +-e e2x b. Yp = 2xe +e2* X- 3 2x C. Yp = 3xe 2…

A:

Q: 2. Determine whether the polynomial 1+ x + ? is a linear combination of P, = 2+x+x², p, = 1-x, p, =…

A:

Q: Expand (y-3x)*. A y +12y x + 54y*x² + 108y²x³ +81x* B y+4y x+ 6y*x² + 4y²x³ + x* y - 12y x + 54y*x²…

A:

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.