By using Laplace transform the solutions of differential equation: d?x + 5+ 4x = e-t, where t-0,x=1 (xo = 1), x1 = 0 dt2 dt

Q: Solve the linear differential equation using Fourier transform.

A: The objective of this question is to solve the given linear differential equation using the Fourier…

Q: Form the second-order differential equation using the parametric definition of y = asine, x = acose…

A: For part (1) We have to find out the second order differential equation of y=asinθ,x=acosθ Use…

Q: 3.2 y" – 2y' + 5 = -8e¬X, y(0) = 2 and y'(0) = 12.

A: Given y" - 2y' + 5 = -8e-x

Q: sin(2t +) dt eu-3 %3D 64

A: Let, I =∫0∞sin2t+π2e2t-3dtApply integration by part ,Ist function = cos(2t) , since sin(π/2+x) =…

Q: dy = ay + by", dt a > 0, 6 > 0, -∞ < Yo < ∞

A: A differential equation is given by, dydt=ay+by2 for a&gt;0, b&gt;0, y0&gt;0. The objective is to…

Q: Transform the following differential equations into start form for linear differential equations

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Q: The complementary function of the differential equation d²y dx² 2 + 3x +y= dy dx 1 is (1-x)²

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Q: Use the inverse differential operators to solve the initial value problem: 2y'' + 5y' + 2y = e2x

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Q: (4r + 5)2 2- + tanzy= dr COSI

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Q: dy 5. dt = e&-t)secy(1+ t²). %3D

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Q: yJzスこナる dy t xJ (A ZXZ+3

A: given differential equation is variable separable differential equation we will first separate the…

Q: Q1} Find the differential of ex²

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Q: Solve the differential equation  2y" + 60y = 2x2y" + 4xy'  . Then evaluate the Legendre polynomial…

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Q: The complementary function(C.F.) of the differential equation(D- 4) y = cos 4r is O (Ci +c21+ czz2)e…

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Q: Solve the differential equation by using the linear equation method 2r dt +4

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Q: Solve the differential equation with subs equation : S y(s) = (s+2)² +1 O e?"(cos t – 2 sin t) O e2"…

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Q: (군2-1) 을 + 2y3 (+ 1)°

A: Given ODE : (x2-1)dydx+2y=(x+1)2 ⇒dydx+2yx2-1=(x+1)2x2-1⇒dydx+2yx2-1=x+1x-1 Which Linear…

Q: y(s) = (s+2)² +1 e2" (cos t - 2 sin t) -2t e" (cost – 2 sin t) A.) B.) e-2"(cos t + 2 sin t) e2"…

A: Correct ans is option A

Q: Solve the differential equation

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Q: 2 (x² + y² + 1) dx + x (x - 2y) dy =

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Q: Check whether the functions which satisfy the following differential equation are linearly…

A: Given differential equation x3d3ydx3+31-αx2d2ydx2+3α2+β2-3β+1xdydx-αα2+β2y=0 Given differential…

Q: Use separation of variables to solve the differential equation explicitly for u. du dt = 3 + 3u + t…

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Q: d²y (2) Check that y = sint satisfies the differential equation dt2

A: We have to solve

Q: Which one of the following is the Exact differential equation ? 1 (x2 +3xy)dy + (y³ +a²)dx = 0 3 (x2…

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Q: Z = 2xy  what will be the partial differential coefficient

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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.