Find the General and Particular solution of dy/dx = 4y ; y = 3, when x = 0

Q: dy x +1 xy %3D dx

A:

Q: Find the particular solution, Using the integrating factor method: dy + In x =- dx y where y(1) =3.

A: Solution: The objective is to find the particular solution to the given differential equation.

Q: (x– x'ye" )dy – dx = 0

A:

Q: Reduce the given DE into Bernoulli's equation: - 2x*y¬ dx 3 y-4 dy_ y5 2x4 y4 dy dx dx 3 3 dy 2x* у…

A:

Q: dy =, with initial condition y(0) =2 is dx y The solution of %3D

A:

Q: Solve D.E using Exact from first order 2.xy dx +(x² +3y²)dy

A: To solve the given differential equation.

Q: Show that y2 +x – 3 = 0 is an implicit solution to dx dy on 2y the interval -o to 3

A: To show that  y2+x-3=0...(1) is an implicit solution to dydx=-12y on the interval (-∞,3)

Q: What is the integrating factor of the D.E. 2y dx + (x- sin vy) dy =0 ?

A:

Q: Find the value(s) of dy/dx  at y=1 given that x2y + y2 = 5.

A:

Q: If y = f(x) is the solution of (-x – 9)dx + (x2 + 10x + 41)dy = 0, f(0) = }In(41) +arctan(5/4), then

A:

Q: dy y- dx ay

A: on solving this we get the

Q: Find dy/dx in terms of t if x = te', y = 4t + 4e* dy/dx =

A:

Q: y_x + y х х — 1 dx

A:

Q: Find dy by +xy-X=0 dy=( )dx

A:

Q: dy = ( e )dx

A: See the attachment

Q: dy ey-x sec y (1 + x²) У (0) 3 0 dx ||

A:

Q: If y = In(2x+3) , then find dy at x = 0. dx

A:

Q: d'y 10ay+25y = 0. dx? 1. Find the general solution for dx

A:

Q: Find dy/dx. x = t?, y = 1-6t dy

A: The objective is to find dy/dx.

Q: Solve the inital value problem from the differentail equation: dy/dx = 1+ y       where y(0) = 1

A: Given: Initial value problem. dy/dx = 1+ y       where y(0) = 1

Q: when

A:

Q: Solve the bernoulli equation dx/dy+(2/x)y=-x^2y^2cos(x)

A:

Q: Solve the equation dy/dx=1-y , given y(0)=0 using modified Euler’s method and find y at x=0.1 and…

A: Given differential equation is, dydx=1-y, y(0)=0. To find the solve the differential equation using…

Q: 1. Solve for y, using the method of successive approximation. dy dx = x + y; y(1) = 1

A:

Q: 4. Obtain the general solution of x? y dy dx

A: By Bartleby policy I have to solve only first one as these are all unrelated problems

Q: Find an implicit solution to the initial value proble dy = y? – 2y, dx y(1) = 3. -

A:

Q: Find the general solution of (x +1)3d²y dx? 1TE + 3(x + 1)² + (x+ 1)y = 6 ln(x +1). dy dx

A:

Q: Find the general solution of the DE dy/dx = y(x – y) / x^2

A:

Q: Find the particular solution to DE:  2xy dx = ( x^2- 2y^3 ) dy ; y ( 0 ) = -2

A:

Q: dy +y=(x-1)y' dx

A:

Q: dy The solution of dx with initia y

A: Introduction: Separation of variables: This method is only practicable if the differential equation…

Q: Zy dx = (x?-1)L dx-dy) %3D

A:

Q: Solve the initial value dy/dx = 1/x2 + 1 - 1, y(0) = 1

A:

Q: Find dy/dx at the given point without first solving for y. xy2 = 27 at (3, 3) xp ||

A:

Q: dy Solve the initial – value problem: = y² given that f(0) = -1 dx %3D

A:

Q: Q20// when x3+y3+x?y xy2+x3 dy %3D dx find the general solution?

A: Given differential equation is  dydx=x3+y3+x2yxy2+x3 the given differential equation is homogenous .

Q: solve using the method of integrating factors. dy dx ==+x, y(1) = 3 х ||

A:

Q: ædy – y(1+ In y – In æ)dx = 0

A: The given differential equation  is changed to  the variable separable form by using the…

Q: dx-(it 2x tany) dy-0

A:

Q: Derive the general solution of dy 1. dx y

A:

Q: dy 1+y3 Determine the solution for the given DE: + = 0 dx xy?(1+x²)

A: Proceed as shown below

Q: Find the General and Particular solution of dy/dx = 3y ; y = 3, when x = 0

A: The formula for integration of fractional function is given by: ∫1x=ln|x|. Given: dydx=3y ; y=3 when…

Q: Find the particular solution of (2x²y² + xy' )dx + 3 y? dy 0 that satisfies the condition y=1 when…

A: To solve the following differential equation

Q: dy Find the solution to dx 5xy which passes through the point (0, e). (In y)? y =

A:

Q: Find the general solution to the following DE. y +x² dy = 0 dx

A: Given DE, y2+x2dydx=0

Q: Solve the homogenous DE Solve: xy dx - (x + 2y)^2 dy = 0.

A:

Q: Find dy/dx at the given point without first solving for y x2 + 3xy + 11 = 0 at (1, –4) %3D dx II

A: Given: The curve is x2+3xy+11=0 and the point is  1,-4. The objective is to find dydx at the given…

Q: Solve the DE by Integrating Factors 1. y² dx + ( 3xy + y² - 1) dy = 0

A:

Q: Find the solution of dx - (1+2x tany) dy = 0

A: Given: dx-1+2xtanydy=0

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

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.