24 Show that the solution of equation satisfying the condition O T-0, as t0 (1) T-0, for x-0 and x=a for all t>0 (i) T =x, whent-0 and 0

Q: Verify that the given function y is a solution of the initial value problem that follows it. y(t) =…

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Q: how can i show that  t/(1+t2 )-tan-10  algebraically?

A: Let gt=t1+t2-tan-1t

Q: 21. Determine the largest interval on which a unique solution of the following initial value problem…

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Q: 9. Use the Secant method to find an approximation to the solution of sin(x) - e-* = 0 in [0, 1]…

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Q: Is the ODE (sin(x-y)+1)dx=(sin(x-y)-2y)dy satisfied by the implicit solution x+y2=cos(x-y). Show…

A: An implicit function, however, is an equation that defines a relationship between two or more…

Q: 1- Solve = cos x + y, where y = dy dx 2.0 at x 0 take step size h = Ax= 0.1 and solve for 0 ≤ x ≤…

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Q: 11) fx-In x dx In x- 2 4 (ans. : -+c) 12) fx- tan'x dx (ans. : 2 -tan"l x -(x- tan"" x)+c) 2 13) fx'…

A: 11.Given,∫x.In x dx

Q: 5. Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that f(x): = X cos x has a…

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Q: By using first fundamental theorem of calculus. Solve the problem 1.) Suppose f(x, y) = S*3 If fx…

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Q: Solve the initial-value problem for y as a function of x. (16 – x)- dy = 1, y(0) = 5 dx ((1 - D- -…

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Q: 2. Find the particular solution to y " = sin(x) given the general solution y = -sin(x) + Ax + B and…

A: The general solution to the differential equation y''=sinx is y=-sinx+Ax+B

Q: 6. Find all the values of z satisfying sinh z = = -j1.

A: What is Hyperbolic Function: The hyperbolic functions in mathematics are comparable to the…

Q: 1. F (x) = sin x+ 2cos x – 5 %3D 2. G(x) = 3e* – 7log;x – 2 * 3. H (x) = 4sec x + 5tanx 4. Z (x) =…

A: Since there are multiple questions. We will solve only the first three questions. If you want to…

Q: Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n…

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Q: Find f(t). f(t) = exp(-3t) sin(t) exp(t) sin(3t) exp(3t) cos(t) exp(-t) cos(3t) exp(3t) sin(t)…

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Q: 2. Find the particular solution of sin y(x+sin y) dx +2x² cos ydy = 0 :3(-1) = 2

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Q: -1-3x+ e3X ) im x>0 hint: L'Hopitals Rule - cos(x)

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Q: 1.4 Compute the value of ₂ (sin x − log x+.e* ) dx using Simpson's th rule. 8 0.2

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Q: The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t = tan(x/2)…

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Q: Show that cos x = x has a solution in the interval [0, 1]. Hint: Show that f (x) = x − cos x has a…

A: Consider  Where x belongs to the interval [0, 1] Since x and cos x both are continuous on [0, 1].…

Q: X 1) f(x) = x6 + 4x + 2 I NIX - 3) f(x) = ln(x5 - cos²x) 5) f(x)=xsin x + πT x5 -√x - In 3 3 2)…

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Q: дz If x² sin(2y - 5z) = 1 + y cos(6zx) defines z implicitly as a function of x and y, find [Show…

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Q: 4. Obtain the particular solution of (D² + 4) y = sin x + sin 2x

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Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

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Q: iFind the general solution of the equation sin4x 19. Find the general solution of the equation cos2x…

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Q: -x² 9 d. f (x) = xe [0, 5]. e. f(x) = |x² − 4], [0,3]. sin x f. f(x) = = [-ㅠ -π, π]. x² + 1

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Suppose that Mdx + Ndy 0 is an exact equation, and M and N are both homogenous functions of degree n…

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Q: 1-2x²=1+x+x²³ 2²-2²-1+2+ -2(-1) (2n + 1)! x²+1 sin x- ---- cos x=(-1). - (2n)! −2+4- 6! tan 'x-…

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Q: Example 2.13. Obtain graphically an approximate value of the root of x = sin x + T/2.

A: Please find step by step solution below

Q: The approximation of the solution x of the equation x In(x + 1)-x-2 0 accurate to within 10 using…

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Q: 12) The solution of 2lnx-In(x+ 2)=In2 is a) 0 b) 1 c) {-1,4) d) 4 e) поп 13) sin( 2 csc"1(2)) = b) -…

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Q: This problem deals with functions defined by f(x) =x + b sin x, where b is a positive constant and…

A: Given,   f(x)=x+b sin x  y=x+b :-Tangent to f(x)

Q: 1. Use fixed-point method to locate the root of f(x) = sin(vx) – x Use an initial guess of xo = 0.5…

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Q: Solve the problem := (1+ 4x)/y over the interval from from x = 0 to x = 1 using a step size of 0.25…

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Q: Find L{(t – 1) (2 – 5 sin 3t)} . O 2 5s 30s - 82+9 (s2 -9)² 2 15 15 - - s2 (s² –9) $(s2-9) 15 15 2…

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Q: 4) One of the solution of the equation y"(x) + p(x)y' (x) + q(x)y(x) = 0 is given by yı (x) =…

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Q: Aitken acceleration method

A: Given: A function is given by f(x)=1-4x cosx +2x2+cos2x To find: The solution of fx=0 starting with…

Q: Solve the problem: u – kuxx = e-t sin x , 0 0; satisfying the conditions u(0,t) = 2n, u(t, t) = 4n,…

A: Let the transformation ux,t=vx,t+Ax+B ...............(1)uxx=vxxut=vtthe problem ut-Kuxx=e-t sinx…

Q: 4) Differentiate each of the following: a) y = - cos²x c) f(0) = sin(20 — π) e) y = (52)²x g) y =…

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Q: [9] Find a 27-periodic solution u(x) of 5u"(x) + 3u(x) = f(x) where f(x) is a 27-periodic function…

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Q: (4) The general solution to (x +3)y" +5xy' - y = 0 converges at least on and is y = Co x2+ r6 +...…

A: 4.  We have differential equation x2+3y''+5xy'-y=0  now take a power series y=∑n=0∞cnxn…

Q: 19) Find [sin( x9+ 9x) ]' = _by Chain Rule A) 9x8sin ( x9+ 9x) C) 9(x8+1) cos x 19) B) -9 x sin (…

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Q: y'+ytan(x)=cos^2(x) ,      y(0)=-1

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Q: Find the solution to the initial value problem for f(x) = 0 and g(x) = 5 sin 3x. q². - 00 0, u(x,0)…

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Q: 33 2Vx- f (x) (1–3t) (t³-8) T Sin sin 2x + Ve2x + 2x – In e, x + 1 - 1-x g(t) = t # 2 2-t

A: Given:

Q: 9 Solve: Solve Sut subject to + bux = 0 u(x,0) = +x² зик + 2х их = 0 subject to ✓****/ Rx [0,00) ản…

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Q: Given that f(x) = V3 cos 5x+sin5x. (a) Express f(x) in the form Rcos(5x-a) where R>0 and 0° < a…

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Q: 1. Solve the initial value problem. dy -= f'(x) = x* - x³ +x – 1, f(0) = -3 dx

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Q: If Newton's method is used to find the critical number of f(x) = a® – a³ + æ² – 2x with initial…

A: Image is attached with detailed solution.