Determine whether fhe e Xaut . i7 it is exact, solve it. given differental eguation tosk -2kg) Sinces gco) =1 %3D dx

Q: Using the fomat of dy/dx below, find (A +B+C+ D). dy 40t? + At +B dx -Ct? + Dt + 3 ||

A:

Q: Given the expression sech ey +cosh ek = In xy, find the value of dx when x = -63and y = -97.

A: Given,  sech e2y+cosh e2x=ln xy

Q: dy If e"y – y? = e – 4, then at x = and y = 2, 2 " dx - ||

A:

Q: Q:2, Prove thunt x (1+x)"dx 306

A: Given:To prove that ∫01x(1+x)16dx=1306

Q: Given that 2x2 - 5y = 3xy. Find the value of dy/dx at the point (-2,2)

A: Given : 2x2 - 5y = 3xy

Q: If x° + y = 65, find the value of at the point (4,1). dx? dy at the point (4,1) is- 2 dx The value…

A: x3+y3=65 Differentiating with respect to x, we get 3x2+3y2·dydx=0    ∵dxndx=nxn-1  &  dcdx=0,…

Q: Complete the following statement. If dy/dx is small, then smallchanges in x will result in…

A:

Q: Use Gaussian Quadrature with 2 steps (n=2) to approximate -5 0.2 dx, xe' which of the following is…

A: According to Gaussian quadrature with 2 steps, ∫abfxdx≈c1fx1+c2fx2 Where…

Q: Given the e dz nd y, find ar

A: Given: xlny=zArctan3zy

Q: For which value of a the equation dz dy dx =2 does hold? O a. 2 O b.3 O C. 4 O d. 1

A:

Q: Exercise:solve the following different D(x+ ye)dx - xe dy = 0. %3D

A:

Q: Use Euler's modified formula to find an approximate value of y whenx = 0.3, given that = x+y and…

A: Given  dy/dx = x+y and y(0)=1 To determine y(0.3) using Euler's modified formula

Q: Simplify the expression shown.

A: Given:

Q: For what value of c does dx 1? 10 X

A:

Q: Solve the following using exact equation or linear whichever is applicable. 1. (х + у) dx + (х — у)…

A: 1. An equation of the form Mdx+Ndy=0 is exact if My=Nx. Here My is the partial derivative of M with…

Q: Find the values of a and b that make following D. E is exact ( - 4) dx + (xyo + 1) dy = 0 x2+2

A: Remark: A differential equation of the form M(x,y) dx + N(x,y) dy = 0 is exact if and only if dM/dy…

Q: Given that S" 4Væ dx = 152, what is fo*4Vt dt ? 3 )

A: As we know that;  the value of definite integral will not change if independent variables changes,…

Q: Use the trapezium rule, with 4 strips, to estimate ? e−x2 dx on [0, 2]. What is the maximum error?…

A:

Q: S = ÷ S gle) de, then 9 x /1 - xª dx 4

A: The question is taken from the calculus in which we have to solve the integral of given question We…

Q: √ay-x² So Sie So dz dy dx

A:

Q: The sides of the rectangle below change according to = 1, = 34. What is dx/dt at the instant when x…

A: Given that the side of rectangle changes below, dzdt=1 dxdt=3dydt⇒dydt=13dxdt…

Q: What is S ØQ,(x)dx if the given equation is dy y = 2xy?e¬x? | dx Select the correct response: -x2…

A:

Q: Use the trapezoidal rule to find A- using the indicated value of n. dx; n = 8 3 3x +3 A, = (Round…

A: We will evaluate the integral by using trapezoidal rule as shown below

Q: While evaluating the approximate value of x2 dx, using Trapezoidal rule, taking 3 h = 0.5, the value…

A:

Q: e Given to 9. Ila,b)=)-0∞ 3(ax?)dx e

A: I could not find what to do after your steps. So I thought of a different process. I hope this…

Q: Evaluate 2z dV, where E is the solid hemisphere a + y? + z² 0. E

A:

Q: Suppose a E R, where a > 0, a # 1, what is[a"]? dx a" In(a) © xa²-1

A:

Q: While evaluating the approximate value of x2 dx, using Trapezoidal rule, taking h = 0.5, 3 the value…

A: Given integral: ∫36x2dx h=0.5 To find: the value of N=?? [no.of sub-intervals]

Q: If the approximated value of , 16x³ dx using Simpson's rule is 260.03, then the error in the…

A:

Q: у?dx + (ху — 1)dy %3D 0

A:

Q: (х — 2у)dx + (у — х)dy %3D C

A: Given differential equation x-2ydx+y-xdy=0 It is of the form Mdx+Ndy=0 Here, M=x-2y and N=y-x…

Q: The approximate value of | dx by using Simpson's rule is 0.3480, then the error in the approximation…

A: We have to find error.

Q: The point of intersection when the coefficients of dx & dy are equated to zer of the given DDE 『うy」。…

A:

Q: 2. (2ху — Зх?) dx + (x? + у) dy 3D 0

A: The differential equation is (2xy-3x2)dx+(x2+y)dy=0. Let P=2xy-3x2 and Q=x2+y. To know whether a…

Q: For which value of a the equation dz dy dx =3 does hold? Oa.2 Ob.0 OC.3 O d. 1

A: This question is about application of integration

Q: For what value of c does dx = 1? J10 x4

A: To find the value of c that satisfy the given integral.

Q: Given r = 15 In(t) and y= 225 t then find dy dx d'y da?

A: Given that x=15lnty=225t2

Q: Find the values of "a" such that f(x,t) = e ax + 6t satisfies the equation of 2f ot dx? smallest…

A:

Q: (х5 + Зу) dx — х dуy %3D 0

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 24. (х? + 2х + у) dx + 2dy %3D 0

A:

Q: (a) Evaluate by solving the work for (i) Sxe-*dx.

A:

Q: d Suppose a E R, where a > 0, a ± 1, what is[a*]? dx

A:

Q: For which value of a the equation SSS dy dx dz 1 2 does hold? O a. 0 Ob.1 O.-1 O d. 2

A:

Q: 1 dr rVx* – 4 #8.

A: The given integral is ∫1xx4-4dx. Let u=x4-4. Then, du=4x3 dx. Apply the substitutions and evaluate…

Q: Use the equations to find dz/dx and dz/ay. e? = 8xyz az 1 ax y az 1 %3D ду II

A:

Q: While evaluating the approximate value of | 2² dx, using Trapezoidal rule, taking h = 0.5, the value…

A:

Q: 8. (y + 1) dx + (4x – y) dy = 0

A: Given Equation is y+1dx + 4x-ydy = 0

Q: Given y is the square root of x. Find dx/dt when y=2 and dy/dt= 1.75

A:

Q: 1.5 2 2.5 3. 5 f (x) 12. 0355 18. 0022 22. 4523 32. 3452 69.0998

A:

Q: Given that y = px? – qx (where p and q are constants), find dx2

A: