Use the Runge-Kutta(2) with h=2 to approximate x(4) for the IVP x'=x?-t+1, 23154, x(2) =2. OA 31 O B. 34 OC 23 O D. 66

Q: Q17: Find the indefinite integral: Sezt (e2x + 1)° dx

A:

Q: Given a6x CosT+Sy - .3x. -Siny+ 10x-e -*, defermine (1) T'=S(T) ax T'-

A: Given:T"=6x2y3-cosx+5y2-siny+10x2-e-3xTo determine:i  T'=∫T"dxii  T'=∫T"dy

Q: Solve the following ODE by introducing integrating factor on the process of your calculation: x dy +…

A:

Q: dy Find for ( In (t), at t = 8. dx (Give an exact answer Use symbolic notatio

A: Here x and y are given in terms of t. So to find derivative of y with respect x we have to find…

Q: f(e) = Given r2 + 14x + 40 dx 1+ cos2 (x) At what value of t does the local max of f(t) occur? %3D

A:

Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x – sin ry; y = 9t t %3D SSEVS Enter…

A:

Q: Find the DE by eliminating the arbitrary constant  y = A+ bex

A: Given equation  y=A+be^x Where A & b are arbitrary constant.

Q: Hiw Solve y=Jx+y' for X=oco.2) 2 by given Xo=0,9o=0· Rung Kutta methood Por 0.0.E (first ordey)

A: Runga Kutta First order method is also known as Euler's Method.

Q: I5/Evaluate using Integration by partts, Substitutionjor both if necessarye tan casa) dx Express…

A: The objective of the question is evaluate the indefinite integral.

Q: a - Find h (Stet sinh t sint dt)

A: The objective is to find ∫te-3tsintsinhtdt It is known that, sint=et-e-t2isinht=eit-e-it2…

Q: dx When evaluating the definite integral / Te why must you 16 – x2" choose the antiderivative–coth…

A: Given:              ∫68dx16-x2 why must you choose the antiderivative 14coth-1x4 rather than…

Q: F. Solve the following by Substitution Method. 1. y(x tanx + In y)dx + tanx dy = 0 dy %3D

A:

Q: Q9/ use the chain rule to express dy/dx in terms of x and y and choose correct answer. 1 x = t2 at t…

A:

Q: Solve the following DE by using appropriate substitution. Evaluate y(x) explicitly. an dy Jy – 5x +…

A: Consider the provided differential equation, dydx=y-5x+4+5 Solve the provided Differential equation.…

Q: 12 Which expression represents the trapezoidal approximation T3 to the integral sin (V7) dx?

A:

Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

A:

Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: Use appropriate substitution to solve the following (iv) zy" + (y/) 0. %3D

A:

Q: Find the Gcneral Solution of the ff.: * u sing Homogen cous, Exact or Non -Ex act Formula. +)…

A:

Q: Find the value of following the integral: ☎ COS²T -π1+a* S². dx,a>0

A:

Q: E valauate the JJ x +2xy +ydy dx when step size of x-0.2 and step size of use the Trapazaidal Rale…

A: given I=∫01∫02x2+2xy+y2dydx with  h=0.2 let x0=0.2 , y0=0.5 let fx,y=x2+2xy+y2 substituting the…

Q: Use substitution to evaluate the indefinite integral | cos³t sint dt. [Hide Solution] cosʻt + C 4

A:

Q: 2xy dx + (x2 – 1)dy = 0 %3D

A: This question is related to differential equation from calculas . We solve this problem using…

Q: [secvadx 9. sinx+cosx dx 10. cosx

A: We have to find the integration by substitution.

Q: the current in an electric circuit is given by di Ri +L==0 dt 18- where R=10 ohm and L=0.2 henry…

A:

Q: At a website, the waiting time X (in minutes) bet ween hits has pdf fx) = 4e ", I20 Ar) = O…

A: Calculate the MGF using the formula.

Q: Use the intormation provided and the totas differential t0 make the given approimation fL나, a)- 13,…

A:

Q: Q2]Using Simpsons1/3 rule for evaluation of sinh(e¬*) dx use n = 4 andwork to 5 decimal place?

A: The formula for Simpson's 13 rule is: ∫abfxdx=∆x3fx0+4fx1+fx3+...+fxn-1+2fx2+fx4+...+fxn-2+fxn Here,…

Q: Find f. (Use C for the constant of the first antiderivative, D for the consta f"'(t) = Vt - 3 cos(t)…

A:

Q: 9. dy dx (xy + 1)2

A: We have to evaluate the iterated integral given below: ∫01∫01 xxy+12dydx. First we will evaluate the…

Q: D.E Poll owing (1+y)dx= (bany -x) dy Solve the %3D

A:

Q: let (t) = re" for 0<t< 2n. Compute tan z dz.

A: Here we use the residue theorem to solve this problem.

Q: (d) e" cos x dx

A:

Q: Find f. (Use C for the constant of the first antiderivative, D for the con f'(t) = Vt - 6 cos(t)

A:

Q: Hiw@ Find dy for the dollowinge りょ CasX +x+ 2) 1 = TE よ + Sec( x) TT InX + T +linx)

A:

Q: 22. Given that sinh 2 =, the value of cosh z is A. +- В. D. 4

A: Given: sinh x=34

Q: Find the value of integral | (22 + y² + 2)ds, where C is parmeterized by F(t) = (cos(4t), sin(4t),…

A:

Q: Find the f(x)=6" locol mayt local miu for te t St -14 dt COS 'x)= x + Sx -14 cosz t) tI 2. %3D

A:

Q: dy of the following functions. dx Find X. a) y = eV cosh¯1 %3D

A:

Q: By the even extension method applied to the function f(x)= e-16z, where a > 0, the value of the…

A: The given function is, f(x)=e-16x,x&gt;0

Q: (ei-e) dx +x cosh udu = 0 when x = 0; u = 0 1. %3D

A:

Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

A:

Q: Can you help me step by step?

A: Differentiate the given function with respect to x,

Q: owing ODE is exact and solve for x(t). dx - - xtan(x) + sec(t) =0 x( dt Where a = (1+Q) with Q being…

A:

Q: (e) S x³ cos(x²)dt (hint: use substitution first) VT/2 COS

A:

Q: Use Green function to Solve the following IVP 44't3y= flx) i yco) = 0 ,y(6) = 1 where X <o f (a) =…

A: Consider the given information. 4y''+3y=fx And, fx=0                   x&lt;0cosx        0≤x≤4πex…

Q: Solve exactly 1. u(x) + f or approximately the following four exercises using Schmidt's method.…

A:

Q: Calculate SN given by Simpson's Rule for the value of N = 6. 1 cos (4x?) dx (Round your answer to…

A:

Q: Calculate SN given by Simpson's Rule for the value of N = 6. cos(3x²)dx (Round your answer to six…

A: given integral :