b) Using Laplace transform, solve the system QUESTION 1 M & UTM a) By using the Laplace transform, solve the following differential equation 5 UTM 3 6 UTM 6 UTM y" + y = 1 – H(t – 37), y(0) = 0, y'(0) = 1. 5 UTN M UTM 6 UTM - b) Using Laplace transform, solve the system UTM & UTM 6 UTN M & UTM & UTM & UTM dx - y = 1, UTM & UTM 6 given that x(0) = -1 and dt dy + x = e' – 1, & UT dt M & UTN & UTM & UTM 6 UTM %3D & UTM & UTM s UTo & UTA & UTM & UTM 8 UTM & UTN

Q: c) u' - 6u = 6 d)-1 Q10) The singular point (s) of (x + 1) y' + x²y = 0, is (are): c) 0 b) 0,-1 a)…

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Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

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Q: Solve the system dx dt with the initial value -4 [3] -3 x(0) = -11 9 [2:]- -6 4 x(t) = X

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Q: Write the given second order equation as its equivalent system of first order equations. u" – 7.5u'…

A: Given second order differential equation is u''-7.5u'+1.5u=-3sin(3t)...(1), u(1)=0 and u'(1)=1.5.

Q: The orthogonal trajectories of y = ce5z where c is arbitrary constant. is_ O z+ 2C = 5y O -2x + 2C =…

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: we have a second-order linear non-homogeneous differential equation: mz'' + 5z' +120z=gm where g=32…

A: The objective of the question is to solve a second-order linear non-homogeneous differential…

Q: x' + 2x + y =sin (t) y' – 4x – 2y = cos(t) x(0) = 0, y(0) = 1.

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Q: A motor and geartrain used in a servo system are operated with a steady voltage and the output of…

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Q: Q7) L(y") = a) s²L(y(x)) + sy(0) - y'(0) c) s²L(y(x))-sy(0) - y'(0) b) s²L(y(x)) + sy(0) + y'(0) d)…

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Q: Some sixth order homogeneous linear differential equation with constant coefficients has the…

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Q: Z₁' (t) = -6₁2 + 1.12₁ -0.822 Z₂²' (t) = -13.8 +2.12, -1.222 Z₁ (0) =11 Z₂₁₂ (0) = 4

A: The given system of differential equations are as follows.Find the equalibrium point as follows.Put…

Q: = Solve the initial value problem x' by using the fundamental matrix e ( 1 X = Choose one ▼ Φ(t) = -…

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Q: Q.4) The Wronskian W(e~2", e",e²), is: a) 12e b) –12e c) 6e² d) -6e"

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Q: The Kermack-McKendrick equations are first order differential equations describing an infectious…

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Q: a2e ax2 a2e + 16 = 0 ay2 For which 1-0 (0, y) = 0 2-0 (1, y)=0 3-0 (x , 0) =0 4-0 (x, 1) 0

A: Here, we need to solve the differential equation ∂2θ∂x2+∂2θ∂y2+16=0 by separation variables. Let θx,…

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: 1) Write the given second order equation as its equivalent system of first order equations. u"…

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Q: 3D0 i) y" -4y' -4-128=3e^(sx)

A: 1). 4y" - 6y' + 7y = 0 2). y" - 4y' -12y = 3e5x

Q: (1 point) Solve the system 1 6 dx dt -1 6 with the initial value 13 æ(0) = 6 a(t) = %3D

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Q: Question 7. a) Find the unique solution of the system of differential equations dg g+h dt dh g - h…

A: For the solution of the problem follow the next steps.

Q: (b) y" – 2y' + 5y = eª cos 2x, y(0) = 2, y' (0) = –1.

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Q: (1 point) Solve the following initial value problem: d 5 18e³t 12 1/² = (₁-3)* + (1960) 67²), 7(0) =…

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Q: Given below is a description and the differential equations problem/question: Make sure to provide…

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Q: Solve the system of differential equations x' – 3x – 6y ly' = 0x + 3y æ(0) = 1, y(0) = 2

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Q: Onsider the differential equation -2e2t t4 (a) Find ₁, 2, roots of the characteristic polynomial of…

A: We have to solve the second order differential equation  y''-4y'+4y=2e2tt4,t>0

Q: Find the general solution to differential equations 2 1) (-2xy) dx + (Siny-x²) dy 2) dy + 3xy dx = x…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: c) y(x) = c, + cz + Acos3x + Bsin3x Q.6) The singular point (s) of (x² + 4)y" – x y' + 4y = 0 , is…

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Q: The system of ordinary differential equations given by x'1 = ax1 + bx2 , x'2 = bx1 + cx2 has the…

A: We have the given system of ordinary differential equations is x'1 = ax1 + bx2  x'2 = bx1 + cx2 In…

Q: (2) Consider the following vector ODE 2 1 1 Y': × - (D) - - () 0 2 -1 Y + 0 0 0 -1 (a) Convert it…

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Q: Consider the nonlinear time-dependent ordinary differential equation (ODE) y '(t) = y ^2 (t)+…

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Q: 3.b) Eliminate the Ar bitrary Constants in the equation: ( 3.a) Eliminate the Arbitrary Conat anta…

A: We have to obtained differential equation of given curves.

Q: Exercise 7 Find the general solution 1. 6y'dx - x(2x + y)dy = 0

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Q: The population of a community is known to increase at a rate proportional to the number of people…

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Q: a) Sketch by hand a slope field for the differential equation y'= x/y. Use it to sketch the four…

A: We need to find slope field.

Q: Solve the following partial differential equation with the given conditions: 8² u Ju Əx² Ət' u(-1,…

A: We are given the following partial differential equation with the given conditions.…

Q: Write the homogeneous part of the differential equation system, namely f (x) = g(x) = 0 obtained…

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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.