nf(x) = 2x³ + kæ – 9, and the remainder %3D -

Q: Find the d. c. of 5x³ from the first principle.

A:

Q: r2V6 x(4 + x)šdx /24

A: To evaluate : ∫2426x4+x13dx

Q: dx x4 + 4

A:

Q: Find the general solution by variation of parameters y" – 10y' + 25y = x3 |

A: Given: y''-10y'+25y=e5xx3

Q: (D² + D)y =x+| ;

A:

Q: Q6. Find the general solution using variation of parameters of y" + 4y = 8tant

A: We have to find the general solution of the given differential equation. For this, we will consider…

Q: In the given question , find d2 y /dx2implicitly in terms of x and y :- x2 y - 4x = 5

A: Given that, x2y-4x=5

Q: Solve for y in terms of x. 9x + 3/2y = 14

A:

Q: fy = √2 – 3x², find d'y dr2

A: Given query is to find the Indicated derivative.

Q: 4* = 32x+1 %3D The value of X in this equation is:

A: Consider the given equation. 4x=32x+1 Take log on both side of the equation. ln4x=ln32x+1

Q: Solve the equation using Reduction of Order (D² - 5D + 6) y = 2e* Oy=e+c₁e²x + 2c₂e³x Oy = √² + ₁³x…

A:

Q: √= - 4x + 43 x² 11x + 18 dx = +C

A:

Q: solve for (D³ -9D)y=0

A: If roots m1,m2,...,mn of the auxiliary equation is real and distinct then complete solution is…

Q: c2 Find (4x + 3y)°dædy

A:

Q: dy = 6x(y – 1)2/3. dr

A:

Q: Find the solution. y'- y = -xyl/2

A:

Q: So* - y-³) dy 2.

A:

Q: Solve the fallowing: X+3Y=40+ 1 X-2Y=D9

A: Let's solve equations.

Q: 8. (D2- 2D+ 1)y = xlnx

A:

Q: Find the general solution of tx -3x = t³+2t for t> 0.

A: Given DE is  tx'-3x=t3+2t .......(1) We find the general solution of (1).

Q: f"(x) = 5x2 + 7x – 19 %3D p(5)(x) =

A:

Q: 10. (D² – 3D) y= 9x² = 9x2

A: 10) Given Information: Given differential equation is D2-3Dy = 9x2

Q: None

A:

Q: Obtain the general solution. (D^2- 2D + 2)y = 0

A: Using solution of Linear Differential Equations with constant coefficients.

Q: Solve for y in terms  of x. 12x + 3/2y = 13

A:

Q: Find (d) E (X² . Y²)

A:

Q: (Dー)y=0 findyc

A:

Q: Is S Gx² + 5x + C)dx = 3x + 5 correct?

A:

Q: 3. (Dª + 3D³ – 6D² – 28D – 24)y = 0 -

A:

Q: dx x2V9-x 2. S(6x³ + 3x?) e*4x d=

A: Only I do que 1 and 2

Q: Find the consumer's and producer's surplus if for a product D(x) = 16 – 0.006x² and S(æ) = 0.003x² .…

A:

Q: -2 c. [.x²e²²x² dx 0

A:

Q: 4x2 + 4x 7 If y = find: 6 5x dy %D da

A: Consider  y=4x2+4x-76-5x

Q: QR %3D S 36 + 2x 'R 8x - 6

A: Given: A polygon whose all sides are equal. So, QR=RS

Q: E. Find x²+y = 4 %3D

A: x2+y2=4

Q: Find m2T (2x) R S T -

A: Solve for the Angle T

Q: Find d2y/dx2 simplify in terms of x and y x2+y2=4

A:

Q: (c) dx x2 – 4x + 13

A:

Q: If y = 4x2 + 2x4, and x is changed from 3 to 3.01, then the value of dy is.

A: The given function is: y=4x2+2x4 Now, given that x changes from 3 to 3.01. So, ∆x=3.01-3=0.01. So,…

Q: The Yp of (D²+D) y=20

A: Given (D2 + D) y = 20 To find yp(x)

Q: Find the general solution 5. (D² – 1)y = 0

A:

Q: f R(x) = 4x and C(x) = 0.004x + 1.5x + 50,

A:

Q: Vx2 – 4 d.x 3.

A: Please refer the attached image for complete solution.

Q: Find the general solution (D3-3D2-3D+1)y = 0

A:

Q: The population of a colony of squirrels is given by 1500 p(t) %3D 3 + 2e-0.1t

A:

Q: (D² - 2D+1)y=(2+x²)e* .

A:

Q: Solve dʻy - 2x- xe 2x– xe dx² by using the undetermined coefficient method.

A:

Q: Find the d?y/dx2 of the function y=(5x² – 3)(7x³ + x)

A: Given: y=5x2-37x3+x To find: d2ydx2

Q: V16-x² (c) S dx 2х

A: Rewrite the given integral as shown below: ∫16-x22xdx=12·∫16-x2xdx

Q: 1. (D² + 4D + 5)y = 50x + 13 e3x

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.