4) x dy-ydx=(x²+xy-2 y²)dx

Q: Find dy Y= 5In CI+x") 4 dy'=?

A: The solution are next step..

Q: 81 fx, y) dy dx 10 10 O-10 10 1아 1아 -10 10 -10 -10 81 -x F(x, y) dy dx = f(x, y) dx dy

A: we have to change the limit of integration.

Q: 1 dy yi+ yi = 1, when x = 0, y = 4 dx

A: y12dydx+y32=1   when x=0, y=4.

Q: Find the set of solutions (3x – 3y – 2) dx – (x – y + 1) dy = 0. - - %3D

A: Given differential equation is linear, we will use substitution to solve it

Q: dy x³ - 2y² f) 3 Hint: You know two methods that will work! %3D dx 4ху

A:

Q: B: By using Homogenous method solve the first order differentia еquation (1+ e») dx - e"l> -1) dy =…

A:

Q: dx ylnx dy || y + 1 X 2

A:

Q: solve using non-exact (x+4y3)dy - ydx = 0

A: Solving the non exact differential equation

Q: Show that if you differentiate both sides of x2 +2y³ = 6, the result is dy dx 2x + 6y² = 0. Then…

A: Given function is x2+2y3=6 Power rule of differentiation states that  ddxxn=nxn-1 And ddxconstant=0…

Q: 8. Find dy dx' x+2x given y = u³ + 4, u = .2

A:

Q: EXAM Q1-If x= cot-1 VE, y =,-. find dy d2y dx' dx2 at t = 2.

A:

Q: Find aff dy dx² for f(x, y) = exy

A: I have done solution in detail....step by step....go through the solution

Q: 3. Se paration of Varlable s: x(y +1)dx+

A:

Q: 6. General solution is y = x² In x + Ca² , EXERCISE 6. dy 2y = x? dx

A:

Q: dy Evaluate dx at point (4,2) given 3(x² + y²)² = 100(x² – y²).

A: Answer and explanation is given below

Q: Differentiate implicitly to find dy/dx. ²+ y² - y² = 29 dy dx 11

A: This question is based on implicit differentiation.

Q: What is the difference between dy dy and Ay Use an example y = 4x?+ eX to under stand. 4x2+ ex

A: In the given questioin we have to tell about the difference between dydx,∂y∂x and ∆y∆x. first we…

Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate (x' + 1)dx.

A:

Q: 7 xsiny dx + Cx²+1)cosy dy = 0, yC)=TT/2

A:

Q: I. Solve for the General or Particula 1. dy dx = 3x+xy² y+x²y

A:

Q: 2x dx by taking n = 4 1+ x Use trapezoidal Rule to evaluate

A: trapezoidal rule

Q: 3. If y = (5x)sin(3x), then dy dx ||

A: Given the function y = f(x)

Q: sech? dx 1- sech Vĩ tanh Vi dt Vi 2-

A:

Q: (3sin y– 5x)dx+2x² cot ydy = 0 3.

A: Given: 3siny-5xdx+2x2cotydy=0

Q: 14) find the respect of y with respect to x Y=(6x+5)^x dy/dx=?

A: Given function: y=6x+5x Taking log to the both sides logy=log6x+5x We know that logxa=a log(x) So,…

Q: 4. (x³ + 3x – 1) dx 2 5. 4x x2 6. SIy + 1) – (y? - 1)]dy

A:

Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

A:

Q: 1 cone of radius x and height y is given by V = =Tx2 y. Suppose that the 3 dy Find when x = 2 and y…

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Q: •1 fl-x r4-x²-y 16. x dz dy dx 0 Jo 3

A: See the attachment

Q: 1) CSc y di + secx dy =0 CSC y Y.

A: Given query is to solve the differential equation.

Q: Find the general solution by means of separation of variables if: dy = xy -x dx

A:

Q: dy 1.- dx ах — by bx — су

A:

Q: 15) 4S(5x)] = x² , then f'(x) = ? %3D dx

A:

Q: 14 Integrate using trig. Substitution: S dx (49x²+1)²

A: Let, Then integrate by substitution

Q: 2x dx by taking n = 4. 1+x Use trapezoidal Rule to evaluate

A: on solving this we get

Q: Solve by separation of variables (y +1)dy dx+x(y^2 +2y)= x.

A:

Q: dy اذا كانت y = 3z2 + (sin(z وكان = *3ez؟ 4 : أحسب dx

A:

Q: 2X Qul If y = Fird dy e %3D (x? +1) (I+ sinx)

A: We use logarithmic differentiation

Q: 2. Use trigonometric substitution to Vx² – 25 dx integrate: 4

A:

Q: The approximation of I = f(x-3)** dx by composite Trapezoidal rule with n=4 is:

A:

Q: x +y-y° =5

A: The given equation is x2+y-y3=5 We have to find dydx=?

Q: Find the particular solution of y(9x-2y)dx - x(6x-y)dy= 0, when x=1, y=1. To start, let y=vx.

A: The given differential equation isyax-2ydx-x6y-ydy=0, with y1=1It can be written…

Q: 4(3x+ y – 2)dx – (3x + y)dy = 0

A:

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: Solve = 1 +y, y(0) = 0 by Picard's method. %3D dx

A:

Q: y

A:

Q: xydy+(x^2-3y)dy=0

A:

Q: Use Variation of Parameters to solve the DE y" – 4y %3D

A: Given differential equation y''−4y=e2xx Write the auxiliary equation m2−4=0 ⇒m2=4⇒m=±2 Hence,…

Q: (2х + Зу — 5)dx + (3x — у — 2)dy — 0

A:

Q: Show that the antiderivatives are equivalent.…

A: ∫6/(4 + 9x2)  dx = arctan 3x2 + C or arccsc √(4 + 9x2 ) / 3x + C We need to show that the…

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.