QUESTION 4 x"+5t(x')²+3x = 2t x (0) = 3 x'(0) = 4 At = 0.2 Use the Euler method with a time step of 0.2 to estimate x(0.6) Use at least 5 decimal places in your calculations.

Q: y = Arctan ( 2+x 1-2x

A: We have to find derivative

Q: h(x)=3sinh(1–3x² )cosh(1–3x² )

A: Sinh^-1(x)= ln(x+[√x^2+1]) Cosh^-1(x)=ln(x+[√x^2-1])

Q: n(3x)+sin(5x - 4) - 3 Using Centered Differencing. h = 0.002 O 4.86693212 O 4.876145534 D…

A: Equation is f(x) = ln(3x) + sin(5x - 4) - 3

Q: 6) Solve for y: 3"*1 = 9"-1

A:

Q: Given f''(x) = – 9 sin(3x) and f'(0) = – 4 and f(0) = 5. %3D %D Find f() =

A:

Q: 12. If m/PSQ = (6x – 13)' and m/PQS = (x + 5)', find m/PQS.

A: In a triangle PQS,  Angle of SPQ=90 so, Angle PSQ + Angle PQS = 90 6x-13 + x+5 = 90 7x - 8 = 90  7x…

Q: 4. Use a suitable numerical method to estimate , xln(x)dx, using h = 0.4. Use 4 decimal places in…

A: Here we will use right Riemann sum to estimate the integral  Given a function f(x) that is…

Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

A:

Q: (7) coshx + sinh x = e* %3D

A:

Q: 4 3 f(x) = arcsec %3D f'(x) =

A: First simplify the given function than use chain Rule of derivative.

Q: By using the exponential definitions of sinh and cosh. show that cosh (t) - sinh (t)

A:

Q: sinh e/2 dx is equal to e/2 2 cosh e 7/2 + C 2 cosh e"/2 + C O - (sinh e /2) + C 1 O -2 cosh e I/2 +…

A:

Q: (x+2) (2x+1)° * (3x+1) [2] Consider y= where x > 0 dy First take Natural Log of both sides then find…

A:

Q: dy for log, 3* dx = esinh x.In siny Q1/ Find

A: The expression of the function is .

Q: In estimating cos(3x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

A:

Q: Show that cosh (3x) = 4cosh³r - 3 cosh T.

A:

Q: SOLVE STEP BY STEP THE FOLLOWING ODE IN DIGITAL FORMAT y' = 3(y - 10)

A: We have to solve the ODE  y'=3(y-10)

Q: y = Arctan (2x)

A:

Q: x2 - 3x/5 + 1 dx 1/2 3r7/s

A:

Q: If | fx)dx =5 and gx)dx: evaluate (11f(x)+10g(x)}dx =

A:

Q: 2 x + لوا + sech (π) = cot(y) + log2 (tanh(x))

A: Given,            ex2+2y+sechπ=coty+log2tanhxTo find : Find dydx.

Q: e-V2x sinh x sin x x dx

A:

Q: 3. y = In(sec(In 0)) Find the derivation

A:

Q: solve dx dt. (1 = 72 X -2 7 with X (0) = 3 L2

A:

Q: Determine the real root of 8(sin x) e-x- 1 = 0 with x0= 0.30 using Newton-Raphson Method until…

A:

Q: 5 solve dx dt = [72X -27 @=132 [3] with X(6)

A:

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT Show that 1- tanh²(z) = sech² (z).

A: Identities of hyperbolic trigonometric function  cosh2z-sinh2z=1tanhz=sinhzcoshz1coshz=sechz

Q: Runge-Kutta 4th

A: y' = y-x   , y(0) =2here h = 0.1f(x , y ) = y-xx0=0y0= 2y(0.1) = y(0) +16(k1+2k2+2k3+k4)k1 = (0.1)…

Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

Q: Use Newton's method to solve for x with an initial estimate of x0 = 2n with d* < 0.001. Cosxcoshx =1…

A: (cos(x))(cosh(x))=1f(x)=(cos(x))(cosh(x))-1ddx((cos(x))(cosh(x))-1)=-sin(x)cosh(x)+cos(x)sinh(x)⇒f'(…

Q: (17) r/4- x² dx

A:

Q: In estimating involved in the approximation using the Error Bound formulas. For Trapezoidal rule,…

A: We have, , with Approximate the errors bound by using:Trapezoidal ruleSimpson's ruleLet Find its…

Q: Question 24 Find dy/dx if y = evx (A evx/2x B (c) ©e*//x D evx-2Vx

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.