5 Given that 9g(x) – 5æ sin(g(x)) = 18x² – 15x – 25 and g() = 0, find g' (

Q: 4. | e2x cos 3x dx

A: NOTE: You have posted multiple questions, we have solved the first question for you, if there is a…

Q: 3 S² x³ cos x ²dx 6.

A:

Q: 4 b. [√x ln xdx, 1 4 ㅠ C. fx√4-xdx, d. fx sin (2x) dx. 0

A: Solve the following

Q: b) [F(x) then find f(x). If 3 In(x)/ sin(3x) − 3e³ + x² + 3. - f(x)dx= 3 ln([x]) + 3x + C

A:

Q: z = y sin(2x) + (1 + x²)e* + cos x tan¬(y* + 1) In(y6 + 137)

A: ∂z∂x=∂∂xysin2x+1+x2ex+cosxtan-1y4+1lny6+137=∂∂xysin2x+∂∂x1+x2ex+∂∂xcosxtan-1y4+1lny6+137=2ycos2x+1+x…

Q: (b) L = (xD – 4+ 2i)(xD – 4 – 2i)(xD – 5)² and L[y) = VT + sin(2 ln(x)) + 7x5 |

A:

Q: I Eliminate the arbitrary constants -2x 2X Y = C,e cos 2× + Ge sin 3X

A:

Q: 1. Determine the general solution of this equation in terms of C ( sin y- ysin x) dx + (cos x + x…

A: We have the following solution for given ODE:

Q: 6. Suppose you wish to differentiate g(x) = sin²(x)+cos²(x). What is the fastest way to do this, and…

A: Given,

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find (27). = sin e 0 X = 0 and

A: Given 3x2-y2=t2 and y=tsinθ

Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: 1 is 1 H.W Find y' for y = ecosx * tan-1(5x) * (5x² + 1) ?

A: for y , y'=?

Q: Suppose that x2y" + axy' + by = 0 has the general solution of the following form: y = x-(C, cos (3…

A:

Q: 4. Find the general solution of wt Wra + sin(x +t) by using the coordinate method.

A: As mentionsed solving question 4 Given: wtt=wxx + sin (x+t)

Q: 2.4 sin x2 x2 +4 Find the approximate value of the integral dx by using one of the Closed Newton…

A: The given integral is ∫22.4sin x2x2+4dx We will use the trapezoidal rule.…

Q: S(6Vx + 3 cos x - 8)dx

A:

Q: dz 1) Find ifz = 3 cos x – sin(xy),x =y = 3t - dt

A: NOTE*** As per bartleby guideline for more than one question asked only first is to be answered…

Q: Suppose that a y" + axy' + by = 0 has the general solution of the following form: y = x'(C1 cos (3…

A:

Q: sin y = cos x (2 cos y– sin²x)

A: Given siny dydx = cosx (2cosy - sin2x)siny dydx -2 cosy cosx = - cosx sin2x…

Q: 5. Consider the equation: 3x – 2 cos x = 0. Use Newton's method starting with the initial…

A:

Q: 2 X 1 t3 COS 4- x² dx 2 -2

A:

Q: 1. If x = e²" and y = sin(3t), find in terms of t.

A: According to Bartleby q&a I can attempt only one question

Q: Find the solution of the equation = e cos y which tends to zero as x→ 00 and has the value cos y…

A:

Q: Determine Yp using undetermined coefficients: 2. (D2-1) y = e-x (2 sin x + 4 cos x)

A: The solution of the problem is given in the next step.

Q: | 1. Find dx dy for the following functions : 45) y=x' log,(3– 2x) (ans.:3x² log,( 3 –2x)-73-2x…

A: We have to find the following derivatives

Q: 1. Eliminate the arbitrary constants on the given equation: -3 x sin y - x²y³ = C

A:

Q: al equation sin(t) with y( solution for this hen t belongs to ||

A:

Q: Eliminate the arbitrary constant ln y = c, sin 3x + c2 cos 3x + 9x^2 -2

A:

Q: 4. Find a general solution to the equation y' – 3y = e" sin(2x). -

A:

Q: Find the general solution using reduction of order. 1. y''+y'=cos(4x)

A:

Q: 4. Find the solution of the equation = e * cos y dy? which tends to zero as x → 0o and has the value…

A:

Q: 3. fe2x+Inx² sin x² dx = = 2x -+√e²x cos x² dx

A:

Q: 2. xy' -y == y cos 3x

A:

Q: 1. Consider 3x + sin x – e* = 0, using Secant Method with initial points xo = 0 and x1 = 1,…

A: The given equation is; 3x+sinx-ex=0.

Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations

Q: V3 f. sin(2x) 2 tan(x) = 1

A: Solve the problem within the domain first find the inverse and then solve.

Q: 8. Suppose that the tangent line to the graph of ƒ(x) = r0) at r = 1 is equal to the tangent line to…

A:

Q: B) Find dx dzy and if x = sin 3z and y = tan23z dx2

A:

Q: Find the solution of the equation = e Cos y ax ay which tends to zero as x → 0o and has the value…

A:

Q: 9. Find the value of k so that (2y sin x cos x - y+ 2y²e")dx - (x- sin? x+ kxye*)dy = becomes exact.…

A: To find the  value such that given equation is exact  differential equation.

Q: Q4. Given that: z = y sin(2x) + (1+x²)e* + cos x tan-1(y* + 1) In(y6 + 137)

A: Given that, z=y sin2x+1+x2ex+cosx tan-1y4+1 lny6+137 ∂z/∂x is the partial derivative of z with…

Q: 2/solve the differentialequation by using methad af Variation of (complete salution is vequired)…

A: Given equation is y'''+9y'=1cos11x               (i) Let us consider y'=z. Then, eq. (i) is reduced…

Q: Find a particular solution by inspection of d²y dx2 +y = -7+e* + cos 2x – 10 sin x

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

Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: Q1-Find S sin 3x e4* dx

A: let I=∫sin3x e4xdx using by parts I=e4x∫sin3x-∫ddxe4x∫sin3xdxdx simplify I=e4x∫sin3x-∫12e4xcos3xdx…

Q: 1 Evaluate the equation /o x² sin (xy)dydx

A:

Q: Find the General and Particular solution of = 8 sin 4x ; y= 6 when x = 0 dx Find the General and…

A: The given equations,1.dydx=8 sin4x ; y=6 when x=02. dydx=4y ; y=3 when x=0

Q: e3x [7 sin 7x + 3 cos 7x] +C 58

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

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.