2. Solve the following equations: dzy 3 dx = 9, when x 0, y = 0, = 0 a) %3D %3D dx? %3D dy b) 24y 3y 5e* dx = 5ez* dx2 d²y c) dy 4. dx2 + 4y = 3e2x dx

Q: Given that y =5u'+4u and x 1 hence find dy dx

A: Differentiation problem

Q: dy 4x2-х-2 : У(1) %3D 1 dx (х+1)(у+1)

A: Explained below

Q: FIND THE GIVEN DIFFERENTI Homogeneous Eguation ( 3x + 4y) dx - dy -0

A:

Q: If u = x+ 1 t = vu y = t? then, = 0 dy dx dy 2. = x dx dy 3. = 1 dx dy dx 1. 4.

A: (3) We have to find out dydx

Q: which of the following is equation is an exact DE? a. (x^2 + 1)dx + xydy = 0 b. xdy + (3x- 2у) dx…

A: which of the following equation is exact DE? (i) x2+1dx+xydy=0 (ii) xdy+3x-2ydx=0 (iii) 2xy…

Q: Solve the particular solution of the given DE: x(r^3-xy^2+2y^3 )dy-y(r^3+2y^3 )dx=D0 @r=1, y=1.

A: We have to solve given problem:

Q: Find the particular solutions of the following separable equations. 4 — 2х dy dx Зу? - 5' *+1 = 2y –…

A:

Q: What is the point of intersection of the given DE (x + 2y – 1)dx – (2x + y – 5)dy = 0 ? Select the…

A: Given,  DE : (x+2y-1)dx-(2x+y-5)dy=0

Q: Rewrite the equation with the variables separated. dy dx + √y = e* √√y dy √y-1 dy dy = ex dx = (ex -…

A:

Q: Which of (a)–(c) is not equal to s(x, y, z) dz dy dx? IIT ra, y. 2) dy dx dz (a) 13 III ra,y. z) dz…

A: Explanation: Given that,  ∫01∫34∫67f(x,y,z)dzdydx   Concept Used: In ∫ba∫cd∫efg(x,y,z)dxdydzlimit…

Q: dy 2х %3D (Зу + x)— dx

A:

Q: What is the numerical approximation to 1 3 -dx -1 2+x using the basic trapezoidal rule? (а) 0 (b) 2…

A:

Q: Is the following statement true or false? Please explain 1. ∫-cf(x,y)dx = -∫cf(x,y)dx 2.…

A: Consider the given Surface integrals: For x-axis: On reversing direction on the curve changes the…

Q: a) Solve etan y dx + (1+ e*) sec'y dy = 0. sin(3z + z?) b) Find y for y = (6 – z*)3

A: The given differential equations is  and the other equation is y=sin(3z+z2)6-z43 The differential…

Q: If I = , 2x e*dx dy = then 1=

A: Given:     ∫11∫012xex2dxdy

Q: Given z = 3 In(t) and y = 9t then find dy dx dy dx2 |3|

A: givenx=3lnt,y=9t2

Q: Rewrite the equation with the variables separated. dy 3 cos(m) dm dy 3 cos(m)dm dm O ydy 3 cos(m)…

A:

Q: If yo is the particular solution of dy 4x°y, y(0) = 3, %3D %3D dx find the value of yo(2).

A:

Q: Consider the following. 2y dx — х dy %3D 2 dx dy Solve for dx dy dx Is y 3x2 + 1 a solution to 2y dx…

A:

Q: ds?--dt? 2tet dx dz +t2" dx? Calculate the tetrad components 7

A: Solu

Q: what is the order and degree of the equation:   (d^3y/dx^3)^2/3 = x+6 dy/dx

A: Given that: d3ydx323=x+6dydx

Q: The standard form of 3dy-xydx= 3y%e*/3 by Bernoull's equation is: dx A Зе dy xy = 3e**/3,3 dx 3 x-…

A:

Q: Solve the differenrtial cotn- y(y+2y-2)dx - 2(x ty) dy= 0

A: Topic:- differential equations

Q: Determine the solution to this DE: * dy t 3y 2 2 dx

A: an integrating factor is a function that is chosen to facilitate the solving of a given equation…

Q: Given x 13 In(t) and y = 169 t2 then find %3D dy dx dy dæ?

A:

Q: Show that if y = cosx/x , then d^2y/dx^2 + 2dy/dx+ y = 0

A: y=cosxx Differentiating with respect to x, we get dydx=dcosxdx·x-dxdx·cosxx2…

Q: NOTE: Enter the exact answer. (36–z² xy dy dx dz

A:

Q: Show that if you differentiate both sides of xy +4x + 2y = 1, the re- sult is (x + 2) + y +4 = 0.…

A: we have to show that the differentiation of xy+4x+2y=1 will result in (x+2)dydx+y+4=0 and then we…

Q: Solve for if y- Ina 2- y?. da MCQ3.pdf dy 2y +1 dx dy 2y +1 dx dy dæ -(2y+1)x 1 dy (2y+ 1)a TERIRS…

A:

Q: Given x = 8 In(t) and y = 64 t² then find dy %3| dx d²y %3D dx? ||

A:

Q: хdу — dy %3D (3x? — 3х)dx — ydx

A: The solution is given as

Q: 1. a- Find a result by using variable separation for dy dx b- y³y+x³=0

A: Note:- These are multiple questions and acording to our company guideline we can do maximum 1…

Q: 1/2 yee? +4 dy +17y=0 dx2 when Pove then ydy that Sinzx, %3D0 dx

A:

Q: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

Q: 2 In(t) and y=4 t2 then find %3D %3D dy dx d'y dx2

A:

Q: If x u(u – 1)2 and y = (3u - 1)², then what is the value of dy/dx

A:

Q: 3 3 ex dx = e3 - e, use this result to evaluate Given that %3D 7ex + 6 dx.

A:

Q: 2. Determine y so that it will satisfy the equation: d'y_dy dx = 4e* +3e²* dx with conditions y(0) =…

A:

Q: The standard form of 3dy- xydx= 3y e* 4x/3 by Bernoulli's equation is: dx = 3e /3,3 ху A dy B y…

A:

Q: By algebraic substitution, the integral dx dx is converted to: 4+Vx dy y+4 2 dy y+4 ydy y+4 2ydy y+4

A:

Q: Given the set of equations y = Arcsec u , u = Vx Which of the following is dy/dx? The answer does…

A:

Q: if y=u, u=v -1/2 and v=lnx, what is the value of dy/dx at x=e

A: Calculate the value of dy/dx and then put x=e .

Q: What is the value of the arbitrary constant of the given DE (3x + 2y + 7)dx + (2x – y)dy = 0 at…

A:

Q: What is the point of intersection of the given 3y + x – 5)dx – (x – y – 1)dy = 0 (-1/2, -3/2) O (2,…

A:

Q: Obtain a solution to this linear equation. dx − (1 + 2x tan y) dy = 0

A: Given that: dx − (1 + 2x tan y) dy = 0

Q: Rewrite the equation with the variables separated. -ydy + sin(x) = 6 dx dy O = [6+ sin(x)] dx ey o…

A:

Q: Find dy/dx in terms of x and y if ax^2-by^5=c^2. Assume that a,b, and c are all constants.

A: Given equation is-  ax^2- by^5= c^2

Q: Find the solution of the equation dy -y = x dx | subject to the condition y(1) = 2. %3D

A: Given differential equation is xdydx-y=x and y(1)=2

Q: Obtain the solution using Integrating Factors Found by Formulas 1. 2(2y² + 5xy – 2y + 4)dx +x(2x +…

A: First we making exact differential equation then find solution.

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.