2. Solve the following hyperbolic equations using suitable hyperbolic identity. a) 3cosh x + sinhx = 5 b) 3 sinh? (x +2)-6=6cosh(x+2) c) 2cosh (x-1)+10 = 10 sinh(x – 1) %3D d) 2 sinhtx) = 5cosh(x)- 4 %3D e) 1-3tanh2 (2x)+sech? (2x) = -2 tanh(2x) %3D f) cosh2x-13 sinh(x) = -19

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A: The given differential equation is y''+4y=0 the auxiliary equation is D2+4=0 D2=-4D=±2i therefore…

Q: 2.3 Find the general solution of p fanx+q tany =lanz

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Q: 2.3 Evaluate the integral sinh 2 dz, 7 3i (z – 2i)4 2i 2+ 4 where C is the circle |z – 2i| = 4…

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Q: 1) Find the parametric equations of the line that is tangent to circle x² + y2 = 25 %3D at point (3,…

A: Given: Equation of circle: x2+y2=25 and tangent at point 3, -4

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Q: 25. Find x, y, e R from 2coshy - 7sinhx = 3 and coshy – 3 sinh? = 2 %3D %3D

A: Find x and y.

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Q: 16. Use Theorem 12 to show that 2n r=0

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Q: 3. Deduce from the orbit equation (1 + e)ro 1 + e cos 0 that a planet is closest to its sun when 0 =…

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Q: Use your results from problem 6 and the fact that Vz = Vr (cos (*2kz) + i sin(*2kz)) for k =…

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Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

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Q: 29. Find the solution of xcos ydx + tanydy = 0 %3D

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Q: Find the orthogonal trajectory of y = C[cos(5x – 1)]. O y? = In [sin(5x – 1)]² + C O In[- cos(5x –…

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Q: Use Superposition approach to find the genral solution of the following equation: y" – 2y' + 3y = -6…

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Q: 6) Find (cor dy of

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Q: Find the cubic root of z = V27 + 3i in the form of r cis 0. 1 (Hint: tan =

A: Given:- Z=√27+3i To find:-  Cubic root of given complex number

Q: y = 46 tan B3 – 2 = 4¢ tan az – 2 %3D and y = 46 tan B2 +2 = 46 tan æ3 + 2 %3D and hence all the gas…

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Q: Find the residues of sin(2²) at z = 0 and z = π. (sin z)2

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, + 3i.…

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Q: 8:54 1 3. If y = (5x)sin(3x) , then %3D dy %3D dx Type here to search

A: This question is related to differentiations. Solve in 2nd step.

Q: 41. cos(7t/2) dt 0,

A: Explanation of the answer is as follows

Q: Consider the following parametric equation. = 5(cos 0 + 0 sin 0) y = 5(sin 0 – 0 cos 0)

A: Given,          The parametric equation are x=5cosθ+θsinθ and y=5sinθ-θcosθ.

Q: Example 1: Find length of the cardioid r = a(1 – cos 0) %3D | from 0 = 0,0 = 2n

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Q: What is r 1- O Option 1 2 2 sin 0-3 cos 0 3 y = ² x + 1 2 x² + y² = 2y²-3x Option 3 in Cartesian…

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Q: d the area of the surface generated by revolving the curve x =cos (2t), y = 7+ sin ( 2° - xis. .....…

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Q: Consider the parametric equations x sin 2t and y -4+c ost. which of the following dy7 represents 2…

A: We are given that x=sin 2t y=4+cos tWe need to find dydx

Q: ,In sec2(sin2y)dy can be evaluated by writing it as sec2y (A @ In sec2( sin2y) · cos2ydy ®/…

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, 15

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Determine an equation for the sinusoidal function shown. 2. 12 21 Oy = 0.5 cos[0.5(x+ x)] + 1.5 Oy,…

A: The general equation of a sin function is given by; y=A cos(Bx+C)+D Where; A→Amplitude of the…

Q: a) x 3cost-3, y3sint+1,0si<2a x = 3 (ost-3 y = 3smt+| 3 (os (6)-3-0 351n(0)+/= (x,y) 8TY T/4 T/2…

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Q: 1. Use Green's Theorem to evaluate [(3ye* -7 sin (3x*))dx + (5x* +2x*y* +8e*-y* )dy, where C is the…

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Q: Produce three isoclines with appropriate direction markers, and sketch one solution curve passing…

A: given differential equation is…

Q: Find the general solution to the hypergeometric ODE #(1 – 2)y" + (; - 2-) a - - 0. 3 ) y y = 0.

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Q: Example B Consider the inhomogeneous equation Yk+1 – 2yk coS Ø + Yk-1 = Rx, sin ø # 0, %3D

A: Given           yk+1-2ykcosϕ+yk-1=Rk  ,  sinϕ ≠0       ... (1) where ϕ is constant and Rk is…

Q: 1 In AABC, AB = xcm, BC=(4- x)cm, ZBAC=y and ZBCA = 30°. Given that siny show that =D4(v2-1) (5…

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Q: e sec(3x+2) sin(3x+2) dx Evaluate cos² (3x+2) -3e sec(3x+2) + . O 1 ,sec(3x+2) + C 3 1 ,sec(3x+2) 3…

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Q: ,In sec²(sin2y)dy can be evaluated by writing it as sec2y ! / sec²( sin2y) - 2 cos2ydy S. | sec2(…

A: To simplify the given integral.

Q: 10. If e is the acute angle between the surfaces xyz = 3x + and 3x - y + 2z = 1 at the point (1 -2…

A: We have to solve given problem:

Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, ± 3i.…

A: Solution is given as below:

Q: 1) Find the parametric equations of the line that is tangent to circle x² + y² = 25 at point (3, -4)

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Q: The solution of the DE (1+ cot'x)y' = cscx coty is %3D None of these siny + In|cosx| = C cosx + In…

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