Example 6.13. Prove that ge + 8 1+ 4 (i) A (ii) 1 + 8°µ? = | 1+ : 2+A 1 1+ 4 (iii) u = 2V(1+ A)

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: Ⓒ Solve зик subject to + 2x x = 0 u(x,0) = in Rx [0,00) n(x)

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Q: A 3. Find (f g)(x) if f(x) = x2+x +1 and g(x) = x2 - x- 1. %3D %3D O (f 9)(x) = a4+ 2a + 3x? +2x +1…

A: We can find (f·g)(x) as below

Q: a) m - 1 b) m – 2 Q.8) The characteristic equation for y"" + 3y" – 4y = 0 , is : b) 2' = 32?-4 c) m…

A: To find out the characteristic equation.

Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: Q5. Use the method of undetermined coefficients to solve (a) y" + 2y + y = x²e-". (b) у" — 2у + 5у 3…

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Q: 2. Solve for y in terms of x for the following equations: a) In(1- 2y) = x %3D b) In(y- 1) - In 2 =…

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Q: a)How quickly is the water leaving the barrel over the first two seconds? b)Will the water drain…

A: The solution is given below in the next step:

Q: Find the root of the function fx) = x³ - x - 1 using secant method with Xo = 0 and x¡=1 %3D a.…

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Q: 1² cu (u + 4)(u - 5) du

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Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: Assume the MR model: Y=3+4x₁ +5x₂2 + epsilon, with sigma = 5 Select the Excel command that will find…

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Q: a) Solve (6x²e* ,x0 ii. [3 cos 2xsin 7xdx 2x+1 1 10x +5 b) Show that (x² +1)(2–x) Hence, find | 2-x…

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Q: Q.4) The Wronskian W(e~2", e",e²), is: a) 12e b) –12e c) 6e² d) -6e"

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Q: 6. 2a? a x + a x + a x k

A: #7 proof

Q: Solve Q11

A: 11. Given that the series                      x∑m=1∞mamxm-1+∑m=0∞amxm

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d'y + 9x2 + 6x dx2 dy 6y = 1+ x3 dx -

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Q: (c) cos(t+ T/4)8(t) (d) (t+1)8(t)dt + 1)8(t)dt (e) (t – 5)dt +1

A: (c) Concept Used:-δ(t)={0if t≠0∞t=0Consider cost+π4δ(t)=cost+π4.0t≠0∞t=0Hence cost+π4δ(t)=0t≠0∞t=0

Q: a) 12 Q.7) To write the power series £=3 4m as the form -4m a) m - 1 we must shift m to become : d)…

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Q: Q.12) The solution of y" + y' = 0 by using power series method , is! %3! a) y(x) = a, – a,(1-+ b)…

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Q: Q.1) The general solution of the equation e' cos , is:

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Q: Solve

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Q: Solve the following D-E 1) y' +y = sinx dy 2) x - 2y = x°cos4x dx dy 3) x = y + x³ + 3x² – 2x dx

A: **As per bartleby guidelines we are allowed to answer only 1 question or 3 sub parts at a time.…

Q: For the given signal, Sketch: a) x(t) d b) a x(t) dt c) x(a) da ∞ x(t) = 0 -t -1 t-3 0 t 3

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Q: c) y(x) = c, + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is…

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Q: (1) y "'+ y "– 2y = 3+2cosx

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Q: 3) Suppose I want to use a "u" substitution to find sec² (9x + 4)dx. What should I choose for u? O…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: (f) y" - y' + 2y = 3e + 4 cos 2x

A: Consider the differential equation y''-y'+2y=3ex+4cos2x. To find the general solution of given…

Q: 1. The water temperature in degrees Fahrenheit at St. Petersburg, FL can be modeled by f (x) = 12.4…

A: topic - trigonometric functions

Q: Which of the following is/are equal to 13 dr 1+æ4 You may find the following formula useful B(m +…

A: Use improper integral

Q: Q.1) The general solution of the equation y e' cosA a) y(t) =c, +c; x +c,¢ ' de' cosa Re' sinx b) y…

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Q: 1) (10) The equation given below; a) prove that it is complete b) solve [(2xy + 1)dx + (x² + 4y)dy…

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Q: Use Midpoint Rule, the distance travelled during this period is, M, =| v(x, )+ v(x, )+ v(x, ) + v(x,…

A: Definition used – The value of the function at a point – The value of the function at a point can…

Q: Let a and 3 be any real numbers. Assume that there is a function f : R → R that satisfies the…

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Q: (a) Find of: dx (i) e? – x y = cos(2x) (ii) y = (V4x2 + 1 – 5x)

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