d y ( t ) + 2 y ( t ) = x ( t) 1.Determine a particular solution when the input signal is x ( t ) = 12e -3t cos(4t ) u (t) . 2. Determine the complete solution with the initial condition     y(0) = 0 .

Q: Exercise (2): use reduction of order to find the other solution and general solution of the given…

A: NOTE: Refresh your page if you can't see any equations. . the given solution is  . the given DE is…

Q: Sketch the solution curves in the phase plane and the z(t)- and y(t)-graphs for the solutions…

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Q: slove the initial value problem: (dx/dt)-5x=cos(4t) with x(0)=5 find x(t)

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Q: Determine the local stability of equilibrium of the ODE d dt x(t) = x(1−xy) dt³ (t) = y=x².

A: Given, a system of ordinary differential equations:It is required to find the local stability of the…

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A: See the attachment

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A: Given: The system is defined as If a = 0, then

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Q: c) Solve the initial value problem (1 + cos² t). 21) dx dt - x sin 2t = 4t² + 5t +4, x(0) = 2

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Q: Consider the differential equation (D₁) : 2ä(t) — 8e¯x(t) + 5 = 0, x(0) = ln(4) and the relation…

A: If a function satisfies the differential equation and the given condition then the function is…

Q: 2. Solve the integro-differential equation for f(t) t –2f(t) = 2 | sinh(w)f(t – w)dw + 1 2 f'sir

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Q: dy Solve the initial value problem: 4( sin(t)- + cos(t)y dt = cos(t) sin (t), 0 < t < T, y(T/2) =…

A: Here the first order differential equation is given as: 4sinty' +costy=cost⋅sin7t0&lt;t&lt;π,…

Q: Solve by separation of variables: dy dx y²-4 x²-1

A: According to our guideline we are supposed to do the only first question if you want any particular…

Q: 2. Verify that the given differential equations are exact and solve the equations: (a) (4x³y - 15x²…

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Q: -2 | (t2 + 3) cos(5t)dt 0.

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Q: (5) Solve the IVP:dy - y = e* cos(2x), y(0) = 2 dx

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Q: e y1(t) – 6yl(t) + 8y(t) = e2t + sin (t) ; y(0) = 0 ; yl(0) = 1 %3D

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Q: Find the solution for cos(x)" - (1 + x²) – 2xy = with the conditions dx2 1+x2 y(1) = -1, y(2) = 2…

A: Given equation is  cos(x)d2ydx2-(1+x2)dydx-2xy=11+x2 with y(1)=-1 and y(2) = 2 h = 0.25 To solve  -…

Q: A population of birds and insects is modelled by the equations dx/dt = 0.4x (1 - .000005x) - .002xy…

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Q: dx Write the linear DE of order one dr- (1+2rtany) dy=0 in standard form +yP(x) = Q(x) or+xP(y) =…

A: Given differential equation is  dx-(1+2xtany)dy=0 we have to write it in the linear from.

Q: Find the general solution to / + (xy)² = y²e%* .

A: since you have posted multiple question in this question which are not interlinked so i have solved…

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Q: Show that x(t) = (1+t, 1-7²) is a Solution x = 1 4°=2-x and draw the Phase Portiert

A: This is an System of DE question.

Q: dy sin x dx y+2

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Q: 3. Is the solution of (D₁) convergent or divergent? Justify your answer.

A: Given That : Differential equation is  2x'(t)-8e-x(t)+5=0 ,x(0)=ln(4)y(t)=ex(t)-3 To Find :…

Q: y1(t) 6y/(t) + 8y(t) = e2t + sin (t) ; y(0) = 0 ; yr(0) = 1 -

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Q: C) Solve the initial value problem dx (1 + cos² t). 1) x sin 2t = 2t² + 3t + 5, x(0) = 0 dt -

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Q: EQUATION

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Q: = 20t (4) Find the solution of the differential equation (d²y + 4 dy + 4y id F2 idt los 1 y ²101 = 0…

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Q: Solve the differential equation using Laplace transforms. The solution is y(t) and y(t) y" - 2y - 3y…

A: To solve the differential equation using Laplace transforms, we first take the Laplace transform of…

Q: 4) and attach it to the solution. Draw (by ha dt raph the slope held for the equation using…

A: One has to draw the slope field.

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.