Given that y = (a + bx)e¯* where a and b are constants, show that d²y + 2 + y = 0 dx2 dx

Q: 5. Find dy/dx (y - x)? = 2x + 4

A: Given: y-x2=2x+4 To find dydx. Solution: Power rule of differentiation states that: ddxxn=nxn-1…

Q: d/dx (dy/dx)` x=1, , where y = x3 + 2x - 11

A: To find: The value of ddxdydx at x=1. Given: The function is y=x3+2x-11. Formula used: Power rule of…

Q: For the equation, 2y(x^2 - y + x)dx + (x^2 - 2y)dy = 0, what is dM/dy - dN/dx?

A: 2y(x2-y+x)dx+(x2-2y) dy =0M.dx+N dy =0M = 2y(x2-y+x)N = x2-2yNow.            dmdy =…

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…

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Q: e | Vĩ In x dx 1

A:

Q: L, x*e*** dx 3+1

A: 3.1) ∫-12x2e(x3+1)dx Let u=x3+1 du=3x2dx

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

A: Given: dydx=4y

Q: Find dy/dx x = 2eθ , y = e−θ/2

A: Given:  x = 2eθ  and y = e−θ/2

Q: Find dy/dx and d²y/dx2 for r = t2 +t +1 and y = t2 + 2t - 1.

A: given that x=t2+t+1 and y=t2+2t-1 we have to find dydx and d2ydx2 Now,          dydx=dydtdxdt…

Q: Given y+In(-) = e dy then dx x(y+1)

A: Given: y+lnyx=e We know that ddxuv=vdudx-udvdxv2                                                 ..1

Q: Find dy/dx if : Y =x(x/a) + √ a2 - x2

A: Given: To Find:

Q: What's the general solution : (y − 1) (dy/dx) = y(x^2)

A:

Q: Find dy/dx If y ex A 2/א"e ],/איe D-2V B.

A: We have to find dy/dx.

Q: If y=x^2 e^2x then dy/dx is equal to

A: we have,y=x2e2xdifferentiating both the sides w.r.t. xusing product rule,we…

Q: d²y dy y = e * is a solution of dx2 = 0 dx

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Q: : x d²y dy dx² dx + +my = 0, given that

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Q: Obtain the general solution to the equation. 5. dx + (x – v²)dv = 0

A: Given that: dx+(x-y2)dy=0

Q: The equation dy - ydx = [-x*y^3* e^(-2x) ]dx is linear in x but not in y. True or false?

A: Given that dy-dx=-xy3e-2xdx.

Q: Obtain the general solution to the equation. dy 1. y + 2x + 1 dx

A: Given that: dydx=yx+2x+1

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

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Q: dy Find if dx y = 7u + 2 and u = 9x-3. dy dx Enter your ar

A: Given:    f(x) = 7u + 2       u = 9x - 3

Q: Find for y = dx dy dx 1 C

A: On solving this we will get

Q: хе*+2 y = e2x+1

A:

Q: Find​ dy/dx by differentiating implicitly. When​ applicable, express the result in terms of x and y.…

A: Given : 5x+7y=3

Q: If y = 3x+2/x-2, evaluate dx/dy when x = 1

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Q: C. dy b. 4 sin 2x> , y = 2, when x = 2 %3D dx dy С. dx = x + 3+ e2x>, y = -1, when x =

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Q: Differentiate implicitly to find dy/dx. -y2 = 7 x2 + y2 %D .2 dy dx %3D

A: Given that, xx2+y2-y2=7

Q: 1 d'y dy + 5y = 0, subject to y(0) = 0 and y'(0) = 40 dx 4 dx2

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Q: dy Find dx2 4 if y = x cos(x) d²y dx? ||

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Q: dy dzy If y = e2x –2e¬3x, Find at x = 1 dx 'dx2'

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Q: 1 Given y = 3x5 + -, dy is equal to 2x3 dx

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Q: Find 2," dy d²y dx ' dx? d3y and from: dx3 3. x = 1 – t? and y = 2t3 – t2 + 1

A:

Q: Find dy/dx given that y3 + y2 − 5y − x2 = −4

A: We have to find dydx for given equation, y3+y2-5y-x2=-4 We know the formula from power rule of…

Q: d*y dy is dx x dx ferential

A:

Q: What is the solution? dy/dx - y/x =xy^2

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Q: dy/dx of y=e^3x+1

A:

Q: If 3x² + 2xy + y² = 2, then the value of dy/dx at x = 1 is

A: Given that        3x2+2xy+y2= 2 We have to find the value of dy/dx at x=1.

Q: If y = = e2a + e3x, then d y at x = 0 equals dx3 %3D

A: Given: y=e2x+e3x

Q: Find dy/dx and d²y/dx2. x = e*, y = te-t

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Q: 19. Find dy/dx. y = x²

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Q: 4xy dx + 2x²° dy + loy - dx + 15 x y dy=0 t

A: given equation 4x2y dx+2x3dy+10y-dx+15xy dy=0 claim- Find non- exact or first order linear DE

Q: Find the general solution for dy dy +2 + 4y = dr dx? e2= (1+ x²)

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

Q: Determine dx dy if y = r -e' and x In(4f)

A: (1) first we find dydt (2) Second we find dxdt (3) then we find dydx=dydtdxdt

Q: Find dy/dx and d 2y/dx2 if x = 1 + t 2 and y = tln t.

A: Given: x=1+t2y=t ln t   Chain rule for derivative: ddxf(g(x)=f'(g(x)).g'(x) Product rule for…

Q: d'y dy - -2xe dx dx

A:

Q: If y=u³ and u = 4x² - 2x + 5, give dy dx

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Q: Find the general solution, using separation of variables: dy dx

A: The given differential equation is  dydx=e-y-x

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.