Find the charge and current at time t by using Laplace transformation, in L-R-C circuit i.e., d²Q dQ + R- dt with R = 0N, L = 1H and C 1 L- :Q=E(t) C %3D dt2 F with E(t) = d(t) volt and %3D theinitial charge = Q(0) = 0 unit and initial current = Q'(0) : 0 unit. Where, E(t) = delta function.

Q: Convert the following 2nd order IVP to a 1st order system IVP, by viewing y' as a second dependent…

A: Given: We have to convert the given 2nd order IVP to a 1st order system IVP, by viewing  as a second…

Q: y' + z' - 2y = 1 z – y' = t %3D Yo = 20 = 1 %3D -

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Q: = 0; y(0) = 2.2, y'(0) = -8.7, y"(0) = 38.85. O y = (91/150)sin 1.5t - 0.2cos 1.5t + 2.4e^(-4t) O y…

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Q: Use the runge-kutta method to approximate y(0.5) for y’ = te^t-2y, 0

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Q: Determine the particular solution of y"–3y'+2y=4e"; y(0)=-3,y'(0)=5 using Laplace and Inverse…

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Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

Q: solve given equation with Laplace transformation  y'' + 2*y' + 2*y = e-t y(0) = 2; y'(0) = 1;

A: First we will take Laplace transform and then inverse Laplace transform.

Q: Solve the nonlinear 2nd order ODE by reducing it to first order using an appropriate substitution:…

A: The solution is given as

Q: dw Use the Chain Rule to find dt w = 7x°y°z,x = 2t, y = cos(4t), z = tsint %3D 7xy°(12yz -…

A: see 2nd and 3rd step.aa

Q: y" + 2y' + y = te),y(0) = 1,y'(0) = -2|

A: Formula Used: L{y''}=s2Y(s)-sy(0)-y'(0)L{y'}=sY(s)-y(0)L{tneat}=n!(s-a)n+1

Q: Consider the DE y"+exy'+ (sinx) y = ex+2lny then the order of the DE is ✓ and it is

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Q: use Laplace trans forms g - 4 y + g'co)= o 3 y = 6t - 8 , ylo)=0 ,

A: Solve the following

Q: y"-8y'-9y=0, y(0)=0,y'(0)=-22. d^2y/dx^2 = y", solve using Laplace Transformation

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Q: y''+4y=u(t)(t-2) , y(0)=y'(0)=0 find the initial value problem with laplace transformation.

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Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: dy -: y = 6x² – 4x, dt dx = 7,x = -2 dt (5) Find -

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Q: Solve y(x) for the Second Order ODE in parameter form: y"+7y'+10y=6e^3x

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Q: Set w(r, y) = cos(xy) where x = t² and y = el-8t, then dw dt Select one: a.…

A: to find the value dw/dt                   dwdt=dwdx.dxdt+dwdy.dydt                     (1)

Q: Use the Laplace transformation method to solve the system * – 6x +3y = 8e', x(0) = -1 ý – 2x – y =…

A: The solution for the asked question is given as

Q: e 8(t – 3) dt = e^15 cos(31)6(t – 5) dt =

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Q: Example: Sketch the direction field for equation: y' = y(2 – y). (1) Evaluate slopes at several y's.…

A: Slopes of y's yy'=y(2-y)y=3-3y=20y=11y=00

Q: If r(t) = cos(5t)i+ sin(5t)j + Otk compute r'(t)= i+ j+ k and ſr(t) dt= i+ j+ k +C with C a constant…

A: Given, rt=cos5ti+sin5tj+0t k Find the value of r't and ∫r'tdt.