Simplify everything and show that e-SP dx u = c1 dx + C2 .2 We can choose simple values for c1 = 1 and c2 = 0 and plug in u into our guess solution of y2(x) = u(x)yı(x) to get the final formula for reduction of order: e-S P dx dx y? (x) Y2(x) = y1 (x) |

Q: 1. The y-intercept of the function y = 3(x + 19)2 – 27 is а. 334 b. -27 С. -8 d. 1056

A: We will find out the required value.

Q: The linearization of y = (6x- 11)2/3 at a = 2 has the form L(x): = mx +b, Find the values of m and…

A: We have to find out

Q: What is the parent function of y = −(x+2)(x − 8)? c. y=x³ d. y=x² 4 a. y = x 2 b. y=x² O A O B O C O…

A: To find the parent function of the function y=-2/3(x+2)(x-8)

Q: (6x + y2) dx + y(2x - 3y) dy = 0. evaluate

A: The given differential equation is                                    (6x+y2)dx+y(2x-3y)=0

Q: + y²(x+ 1)² = C

A:

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

A:

Q: Find dy. 3 y=³√√x (6-5x).

A: Given query is to find differential.

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: 6. Find (x + 3y)dA where D = {(x, y) | æ² + y 0}

A:

Q: Solve: (x+y)dy-(x - y)dx=0 A. x² - 2xy-y²= B. x² + 2xy + y² =c C. x² + y² =c D. x² - 2xy + y² =

A: The given equation is(x+y)dy-(x-y)dx=0 To solve the differential equation.

Q: 252 EXERCISE 9E 1 Evaluate: a d a [²3x² dx 2 Evaluate: d (10-x²) dx ²(3x²-2+)dx √(1-x) dx b e b e…

A: 1)e) The given integral is 4x2-2x, limit from -1 to 2.  2)e) The given integral is [(3-x) (8+x)]/x4,…

Q: (X²y² + 1)dx +2x²dy =0 use the substitute xy=u

A:

Q: Change (x + 9)? + y? = 169 to x? + y? + Dx + Ey + F = 0. Change x? + y? – 8x – 8y + 16 = 0 to (x-h)?…

A: topic - equation of circles

Q: f(x) = x O A. -2 O B.

A: None of the options are correct, correct solution is given below

Q: Ho Find (yor dy d'y ) and (y or -) for the following functions: dx dx L 2. y= x² (x-1)² 5. y=(x²…

A: We need to find the first order and 2nd order derivatives of the given functions.

Q: d. x+3y = 0 y-4+ 4(x - 2) f. -6x + 4y -7 Find intercent and v-intercent.

A:

Q: // (3x + 4y)dA where Find D D = {(x, y) | x² + y² 0}

A: Given f(x,y) = 3x+4ydA =dxdyarea bounded by the region x2+y2≤4,x≥0. It is a semicircle in the left…

Q: 10. The y" of y = (2x¹ + 4x³)(3x¹ − x³) is - a. 336x6 +420x5-120x¹ C. b. 336x5 +420x4-120x d. 48x7…

A:

Q: The change of the energy efficiency function ( P ) of a factory with respect to uj and u2

A: In this question, we have to find the maximum value for the two-variable function. Here we use the…

Q: Find // (3x + 5y)dA where D D = {(x, y) | x² + y² 0} . Round your answer to four decimal places.

A: Double integration

Q: Evaluate | (r + y)ds, c : x 3t, y = - 3t + 3, for 0 <t< 3.

A: Given: ∫C(x+y)ds, C: x=3t, y=-3t+3, for 0≤t≤3

Q: Solve: (3x? – 2xy+ 3y² )dx = 4xydy O (y – 3x) (y + x) = Ca³ O (y + 3x)³(y – x) = Ca³ O (y – 3x)(y +…

A: Proceed as shown below

Q: 1. xy' – y – 5x* – 3x² + 2x = 0 when x = 1 and y = 2 н. ху' —

A:

Q: c) Find f(-1) if f(0) = 2, f(1) = 9, f(2) = 28, f(3) = 65, f(4) = 126, f(5) = 217. %3D

A: Newton's forward difference interpolation formula is, y(x)=y0+pΔy0+ p(p-1)2!    ⋅Δ2y0+  p(p-1)p-33!…

Q: The linearization of_z = y√x_atx=16 and y=1 is

A: Linearization is defined as the finding of a linear approximation to a given function at a given…

Q: Find // (5x + y)dA where D : {(x, y) | x² + y? 0}

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.