Solve the initial value problem: 9y/" – 12y + 17y = 0, y(T/4) = -2, y(T/4) = 1. Give your answer as y =. .. . Use x as the independent variable. (2x) Answer: y= e (7V13 sin(x – 4x) +26 cos 12 V13 (x - 4x)| V13 (T-4x))| 13

Q: If the following eq. is exact, then solve it (y cos x + 2xe) + (sin x + x²e + 2)y' 0.

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Q: If y = cos¹ (v₁²), X = find dz? 1 Vu² +1 2= ln (2x-3y)

A: Consider the given equations, y=cos-1vu2x=1vu2+1z=ln2x-3y here we need to find the value of dz.…

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Q: Solve the ODE: (3e3 sin y-42y sin(7x)) dx + (e³ cos y + 12y cos(7x)) dy = 0 Entry format: Write your…

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Q: 5.) Scesin 2 sinl 3x) - 5 cos ( 2x))·dx

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Q: On another planet, after t seconds, Cora hurls a projectile with initial velocity vo and angle from…

A: On another planet, after t seconds, Cora hurls a projectile with initial velocity v0 and angle θ…

Q: b) Solve to find if y = Tant VE and t = 4x-2 – secx dz b) if z = sin20, and 0 = [cos(w) + 1]² + cos…

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Q: 37/2 8 cos x dx T/2

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Q: Solve the following equation forz: √8- cos (22) = 3. 0x==²(1) Co OI= cos ¹ (1)-2 Oz=(-1) Ozcos¹ (2)…

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Q: Calculate ㅠ 2 6³ cos² (4x) sin² (4x) dx

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Q: cos(t) dt 2/3sqrt(x+5)^5-10(x+5)^(1/2) +C (5 sin(t) + 9)2

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Q: true or false prove your answer If (an) is Cauchy and p is a number such that for infinitely many…

A: Given that              an is a Cauchy sequence and p is a number such that for infinitely many…

Q: Solve the following equation for y(x): y" + 4y = 6 cos 3x + 20 sin 3x

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Q: 5. Which equation can be solved by referencing the graph below? -1/2 -11/4 3 cosx – 1 = sinx O…

A: The range of both cosine and sine function is .The value of the sine function is zero for all…

Q: Evaluate * 10 x° + sin(x) dx 10 10 1.5

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Q: Solve 4x cos(3x) dx using Integration by Parts. 4x 3 + sin 3x + 4 cos 3x + c

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Q: 27. Evaluate: cos 2) - sin 6 4 /3 /2 2 2 1 V2 V3 2 2 1 V2 2 None of the above. + |

A: Hence option (c) is correct.

Q: Q7. Solve the following equations: 3.2. cos¹ 4x-sin' 4x+x

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Q: Suppose w = 8x² + 2y², X = 3 cos(t) + 9 sin(t), and y = 3 cos(t) — 9 sin(t).

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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.