3. y=x(x-3) Note: y'=: 4x-3 y"3= 2(2x+3) %3D 2 3x3 9x513

Q: 1. у" — 4у 3 2+ 3х — х2

A:

Q: 7. Evaluate Soy4 2 - y dy using Gamma/Beta function.

A: The solution is given as

Q: The general series solution about the ordinary polnt 0 of the differential equation y"+x²y 0 is:…

A:

Q: What is the integrating factor for the linear differential equation 2(y - 4x^2) dx + x dy = 0?.

A: Given:  2(y - 4x^2) dx + x dy = 0

Q: 3. Find for the simplified general solution of (1 + x³)dy - x²ydx = 0

A:

Q: from the partial differential equation by eliminating the arbitrary function z=(x2+y2+z2)

A:

Q: 2. Find the particular solution to y " = sin(x) given the general solution y = -sin(x) + Ax + B and…

A: The general solution to the differential equation y''=sinx is y=-sinx+Ax+B

Q: From the partial differential equation by elimanating the arbiraty function z=f(x2+y2+z2)

A: We have to form the partial differential equation.

Q: [  (1+ xsiny)dx - x2cosydy = 0  ] How can I find the solution "y" of this equation?

A: We shall use basic knowledge of first order ordinary differential equations to solve this question.…

Q: (3) y = ln¯' væ

A:

Q: 4. Find the differential equation of a family of parabolas with axis parallel to the x- axis.

A:

Q: x²(a+x) 2. Family of strophoids with the equation y² %3D a-x

A:

Q: 4) Find the singular points, residual values, ond of +he = (2 function,

A: The given function is f(z)=1(z2+2z+2)3 The singular points are the points where the denominator of…

Q: a particular solution that satisfies the differential equation F'(x)=3x^2 +2x -1 and the inital

A:

Q: 3: The dimensions of a rectangular box are measured to be 75 cm, 60 cm, and 40 cm, and each…

A:

Q: Step 1 Given nonlinear differential equation; bxn-k Xn+1 = Axn + Bxn-k + Cxp-1 + Dxn-o +…

A:

Q: Find the particular solution by means of integration factor method if: (x* +1) +3x(y-1)=0 where y(1)…

A:

Q: 2. Find the general solution of (2x-3y-2) dx-(x-2y)dy = 0

A:

Q: n. ²u

A: Given;

Q: Find the differential equation of the family of circles with centers on the line x – 2y = 3 and…

A: Given:  circles with centers on the line x – 2y = 3and passing through (3, 0).

Q: Obtain the differential equation of the family of straight line with the algebraic sum of the…

A: The differential equation of the family of straight line with the algebraic sum of the intercept…

Q: Obtain the particular solution of (3siny-5x)dx+2x^2cotydy=0 using Bernoulli's Equation. (Complete…

A:

Q: Solve the initial value problem. 4 y(x) = 4 sec(3.x) tan(3.x) ; y(7) = %3D 3

A: y'(x) =4 sec(3x) tan(3x)y(x)=∫ 4 sec(3x) tan(3x) dx3x=t,dx=dt3y(x)=43∫ sec(t) tan(t) dt     =43 sect…

Q: (2xy- 3x)dx+(x² + 2y)dy = 0

A:

Q: 11.Solve dy - x+) y(2) = 2 by Fourth order Runge-Kutta Method at x = 2.5, and x = 3 %3D dx

A:

Q: 3. Determine the differential coefficient of y 2x- 3 when x = 3 Give the answer correct to 3…

A:

Q: y ln x - x ln y = 1

A: ylnx-xlny=1Treat y as yx

Q: (b) Find the differential for y = -5 %3D

A: Giveny=4x-53   ...(1)

Q: What is the value of the coefficient d of the equation y = ax + bx² + cx + d so that it will have…

A:

Q: 6. Why is it very easy to conclude that x2 dx diverges without making any integration calculations?

A: This question is taken from the calculus and sub-topic is improper integral in which we have to give…

Q: 3. The sum of the lengths of the two diagonals of a parallelogram is 18 m. One diagonal is 2 meters…

A: Here we will use two formula  1st Area of triangle  If two sides of a triangle has length a and b…

Q: •1 cln(5) 1- S SmS) xy evx ´dydx r

A:

Q: This problem deals with the differential equation dx/dt kx(x – M) – h that models the harvesting of…

A:

Q: 6. Show that 2y2 dy x² + y2 dx is homogenous equations. Hence, solve the equation.

A:

Q: Find the differential of y² + x = 4.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Solve the problem := (1+ 4x)/y over the interval from from x = 0 to x = 1 using a step size of 0.25…

A:

Q: 2. Find the particular solution of (3sin y- 5x) dx+2x cot ydy = 0 ;y(-1)=-

A:

Q: 9. . sinh 3x dp- 1+cos 3x 2x+9 10. S x² +6x-4

A:

Q: Obtain the differential equation of the family of lines passing through (-1.1).

A:

Q: Particular Integral for the differential equation (D² + 25)y =(cos5x) is given by a. -xsin5x 5 b.…

A: Option; b is correct.  Given differential equation ; (D2  + 25 )y  = cos5x Let D = m; Auxiliary…

Q: Jesaki Inc will sell N units of product after spending $x thousand in advertislhg, as en by N = 74…

A: The given data is: N=74x-x2 To use differential approximation to estimate the increase in sales that…

Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 4. Obtain the general solution of x² y2 = dx

A:

Q: Find the differential equation of family of parabolas with axis parallel to the x-axis and with…

A: The general equation of family of parabolas with axis parallel to the x-axis, with a vertex at a…

Q: In(|(2 +1)"(z + 3)|l) 15x - 13 dx = X (Don't forget to include the constant of 2-2x 3…

A: topic - indefinite integral

Q: What are the Mixture Problems? How these are related with differential Equations?

A: Mixing Problems:  If we will start with a substance that is dissolved in a liquid. Liquid will be…

Q: Solve (5x2y2 O a. b. 2 ln 3 In a In xy² + 17y²) dx (x+2)³(x²+9) y³ |(x+2)³(x²+9) Y - -1 3 tan-¹() =…

A: Given 5x2y2-xy2+17y2dx-x3y+2x2y+9xy+18ydy=0

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.