d²y 1. dx² - dy - 6y = 0, when x = 0, y = 0, and when x = 1, y = e³ dx

Q: 5- 4=0

A: 4. xy'+1+xy=e-x Divide by x both side  y'+1+xxy=e-xx Given deferential equation is of the form…

Q: 3/Sx+9 ニ 3x +13

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Q: 2x -8 g(x) = (x – 4)(x+3)(x –1) х-intercept(s) y-intercept(s) Horizontal Asymptote(s) Vertical…

A: For the function gx=2x-8(x-4)(x+3)(x-1) The objectives are to find: 1) x-intercepts 2) y-intercepts…

Q: We can also derive the other identities below (1.137) sin−¹(z) = −i ln (iz + √√1 − z²), sinh¯¹(z) =…

A: From the given identity there are another expressions, but our aim to establish the given expression…

Q: 1. y(y+k)² In sin(x) = y' tan x 2. y (x-7)y' = xy+3y %3D

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Q: 2.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2хy? + 4 %3D 2(3 — х2)у' ) dy

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Q: [1 -2 -1 1 Let B = |0 [1 1 and let C= |2 3] 1 3 [5.

A: If a system of equation has more unknown than equations then system has infinitely many solutions.

Q: d²y dy +4 dx² + 4y = 0, when x = 0, y = 1, y' = -1 dx

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Q: C. log, b 1 log, a D. If 2ª = then x+y = 0 1 24

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Q: . Find the values of the unknowns which satisfy the following equations: a) (sin x, sin 2x, ln e)…

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Q: 1. (4D5 - 8D4 – 17D3 + 12D² +9D)y = 0 2. (D® – D°)y = 0 3. (D3-D2 - 4D – 2) y = 0

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Q: y" + 3y" – 4y' – 63y = 2sin²x

A: I attached 3 photo, kindly check it.  Thank you.

Q: Use the d'Alembert solution to solve -00 0, u(г,0) cos? r, u(x, 0) = e®+1.

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Q: (a) z + (-5, 7) = (2, 1) (b) 2+ 3i + z = -5 – i (c) z·(2, 3) = (4, 5) (d) Fi = (3, 2) -1,3)

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Q: (1) y+(u3s.n")-40 = 2 6. 2 3a.18b O 368 (b45+5p)+ ?p

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Q: a) z³ =√3+i

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Q: (D' +5D +3D-9)y = 0; when x = 0, y =-1, when x = 1, y = 0 and also as x→ 0, y = 0

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