9. Let y (t) be the solution of the initial value problem y" + y = uz/2(t)+ 36(t – 37 /2) – u2m(t) y (0) = 0 and f (0) = 0 37 Find the value of y A) 1 B) 0 C) 3 D) 2 E)

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Q: C1 and C2 are arbitrary constants. Note: Y1(t) 2t and y2(t) = e2t are independent solutions of y" –…

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Q: Find a particular solution to y" + 8y' + 16y : -7.5e 4t t² +1 Yp =

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Q: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

A: Suppose z is implicitly given as a function of x and y, according to The equation: y−zx3=1−yz2 The…

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Q: Solve the simultaneous ODES (a) x"(t) + 4x(t) + 5y(t) = t²,_y"(t) + 5x(t) + 4y(t) = t +1

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Q: 2. a) Find the general solution of (z²-2yz-y²)p+(xy+xz)q=xy-xz, b) which passes through the curve…

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Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' +y = 0. If W(y1, Y2)(2) = e² , then W…

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Q: The solution of y = 5y + e 2"y2, y(0) = 2 satisfies:

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Q: Give a particular solution for y" – 2y' + y = 3e*.

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Q: 6. Find the general solution to y" – 6y" = 3 – 6e2z

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Q: 2. Find all solutions to the equation y" +y – 10y = 0. Hint: p(A) = X3 + A – 10 = (X – 2)X² + 2A +…

A: The solution of homogenous linear differential equation of constant coefficient is find by…

Q: Solve y'-y y'e" A) y(c- x) = e", y= 0 B) y(c – x) = 0, y = 0 C) y= e", y = 0 D) y(c-x') = e", y= 0

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Q: e a. y; = +e-2= In(e" +1) +e-* In(e" + 1) – 6 2 b. Y, = re2" + e In(1 + e") – e2" In(1+ e") C. Y; =…

A: Option (a) is correct.   See the solution in the attachment.

Q: y₁(t) = et 2e-t and y₂(t) = 2te-t + et are both solutions of nonhomogeneous DE y" + 2y + y = g(t),…

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Q: • 2. Solve by VP: y"' – 3y" + 2y' - et 1+e-x Hint: Answer is y = C1 + €ze* + c3e2x + (e* + 1) -In(e*…

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Q: Q(2): Find the general solution of x³y" – 3x²y" + 6ry' – by = xª In x. %3D

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Q: The function f(x) = |ax - b| + c|x| : x in (-∞, ol where Find the

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Q: 7) A particle P moves along the x-axis in such a way that its acceleration at any instant t20 is…

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Q: Example 5.8. Solve du 0 0, ax2 at for (i) u(x, 0+) = f(x), (ii) u(0, t) = 0, t > 0, (iii) u(1,t) =…

A: To solve: ∂2u∂x2=∂u∂t, 0<x<1, t>0 And, the boundary conditions are: ux,0+=fx, u0,t=0,…

Q: =² + 2y²) = ry, y(-1) = 1 dy O 2n* = y² + a? O a* = 4 (y² + a²) O a4 = 2 (y² + x²)

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Q: X 0 1 2 3 y 4 12 36 108 Write the equation for the exponential relation represented in the table of…

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Q: Let X = {a, b, c, d} and TX = {ø, X, {b}, %3D {b,c}, {a,b,d}} be a topology on X. Let Y = {1, 2, 3,…

A: A function is continuous if and only if inverse image of every open set is open

Q: 6 - Show that x(t) = (C1 + C2t) e¬t is a valid solution to i + 2yi + 7²x = 0.

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Q: Can you Help with this zero rule problem

A: Given,           8x4y0

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Q: ) Give a particular solution for y" – 2y' + y = 1+x² *

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Q: 06. If y(t) is the solution of the ivp {{ S__2e-28 A._y(t) = L-1 B. y(t) = -1 C. y(t) = L-1 s+6 83 3…

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Q: 5. Solve xdx + ydy = xdy – ydx %3D |

A: Introduction :

Q: nd a particular solution to = y" + 8y + 16y= = -15.5e-4t t² + 1

A: Particular integration by shortcut method

Q: Define fct) = {est + e + cast if t 1/2 t>"/2 solve y(3) - 2 y(2) + ý' - 2y = f(t) y (0) = 1, y'(0) =…

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Q: Solve for fazy for f(x, y, z) = 4x³y²z - e²zy¹ + + 4y - x¹6

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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.