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: find the differential equation of y =C1cos(w+C2), w is A PARAMETER

A: To find the differential equation.

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: Consider the differential equation x²y" 4xy' + 6y=0; x², x³, (0, 0). Verify that the given functions…

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

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

Q: 2. How many edges has each of the following graphs: (а) (5 рoints) К10: (b) (5 рoints) K,7; (c) (5…

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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: Q5) find the derivative 1. x = sin and y = sin+ cos if taken together, satisfy the differential…

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Q: Find the differential operator which will annihilate the function 2x + r³ – sin 2r.

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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: v = ) V In(2x-3y

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Q: 5

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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: Find the integrating factor of the non-exact differential equation : (3x²y+6xy+y³) dx+3(x²+y²) dy=0

A: Given a differential equation, 3x2y+6xy+y3dx+3x2+y2dy=0. To find the integrating factor of the given…

Q: Solve the differential equation by using an integrating factor:y/+9y = x³e-9x Oxe-9 + C x²4e-9x +…

A: The given problem is to solve the given differential equation by using integrating factor. Given…

Q: Determine the differential equation that is satisfied by x(t) = c,e3t + cze¬t – te-t

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Q: nd the solution of the differential equation = Z 3 + sin(z) with i dz

A: Given: dfdz=z-23+sin(z)f(0)=2

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

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.