Using Laplace transformation, the solution of the following differential equation y" + 2y = sin(t), with y(0) = 0 and y'(0) = 1 %3D %3D is: y(t) = 3- 3cos (t) + 2sin (t) y(t) = sin (t) This option O This option sin (t) y(t) = "-+ y(t) = %3D 2.

Q: Q1) solve the following differential equation 2- 3- y² (cos x +)dx + (e² + 2yIn(x))dy = 0 (sin³ (x)…

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Q: Form the differential equation by eliminating the constant 'a' from r=2a (sin 0- cos 0)

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Q: The standard form of the following linear differential equation sec(x) y' + csc(x) y = 1 is: O…

A: Option A

Q: Compute y' and y". The symbols C₁ and C₂ represent constants. y = C₁ex sin x + C₂ex cos x y'(x) =…

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Q: Solve the differential equation y"-3y'-4y 0 O y= e3* (c cos 2x + C2 sin 2x) cos 3x + c2 sin 3x) O y=…

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Q: Find a particular solution y, of the differential equation: (a) 2y" + 4y' + 7y = x2 (b) y" + 9y = 2…

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Q: 9. cos(xy) (x dy + y dx) = 0; y(1) = = 10. [y sec2 (xy) + 1) dx + x sec (xy) dy = 0; y (;) =" %3D 3.

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Q: Obtain the differential equation of a parabola with axis parallel to the x-axis. A 3(y")²-y'y"=0 B…

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Q: ; v' = v ]n(y + 2).

A: Given differential equationThe equillibrium solution is obtianed when

Q: The differential equation ty' = cos² (y) is . ...linear, separable, and autonomous. O.nonlinear,…

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Q: Solve the differential equation by variation of parameters. y" + y = sec (0) tan(0) y(0) = c₁cos (0)…

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Q: Q1) Find the exact sol of differential equation xy'+ y 2x, y(1) = 2

A: Given differential equation is xy'+y=2x, y(1)=2 To find the exact solution of the differential…

Q: Verify that the indicated expression is an implicit solution of the given differential equation. 1 (…

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Q: Consider the differential equation for y(x): a) d²y dz² Consider the auxiliary equation for this…

A: d2ydx2+6dydx+9y=0

Q: Find the general solution of the following differential equation: a) t * dy/dt = (1-y^(2))^(1/2).…

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Q: A solution of the Ordinary Differential Equation x?y'' - 2xy' + (x² + 2) y = 0, x > 0 is defined by…

A: 4th option is correct. y_p= xcos(x)

Q: (Siny) (dy/dx) – 2Cosy. Cosx + Cosx = 0  find type of differential equation and get the general…

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Q: Yp = -1 / 5ex - 1/2 (cos 2x) ((ln (sec2x + tan2x)) is the particular solution of the differential…

A: A solution yp(x) of a differential equation that contains no arbitrary constants is called a…

Q: find differential equation of the following equation 1) y' = y-x y+x

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Consider the differential equation y' = 1 - y. (a) Find equations for the isoclines corresponding to…

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Q: Put the differential equation p(t) = g(t) = ty' (t² + 5)y = cos(t) + e3t into the form y' + p(t)y =…

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Q: (1 + cos 2y) dr - 2r dy = 0, y(1) = i %3D Oy = Arctan 2 O y = Arctan O y = Arctan ( 1) D y = Arctan…

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Q: (5) Find the general solution of the differential equation (D +6D + 4)y= cos 2a

A: Since you have asked multiple questions, we will solve the second question for you (Please specify…

Q: The indicial equation of the differential equation x²y" - x²y' + (1 +x)y 0 is: O r(r-2)=0 O…

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Q: Consider the differential equation y' -5x + 7y – 10 (1) By making the change of variable…

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Q: dy/dt = y(1-y) y1(0) = 9, y2(0) = -1 What do y1 and y2 mean? The first and second derivatives?

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Q: Use Laplace transformation technique to solve the differential equation. y’’ + 1 = 2t y(0)=2 y’(0)=1

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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.