5. The motion of a mass attached to a dashpot and a spring as it experiences a force can be represented by dx d?x Fr = -kx Fg = -B- dt Fm = m dt2 As the net force (F) is equal to 1, the following differential equation can be written: FB + Fm + Fx = 1 d?x dx m dt2 -B- kx = 1 dt Where m = 1, B = 1 and k = 6, Solve the above differential equation using the Laplace Transform method at the following initial conditions, x(0) = 0, x'(0) = 0. %3!

Q: 4y" — у 3D хе2

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Q: 4. Classify the following differential equations according to whether they are linear or nonlinear.…

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Q: 34. The general solution of the differential equation dI + 4r = 0, p and q being arbitrary constants…

A: We have to find the characteristic equation first.

Q: 40. Show that the general solution of the differential equation stants, is + 2a f + w°r = 0, where a…

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Q: 2. Match each differential equation with its direction field and give a reason why. 3₁ 0 (a) Y (C)…

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Q: Suppose the roots of the auxiliary equation are at iß. These are unequal roots, the general solution…

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Q: Evaluate the given differential equation (2x + 3)y' = y + (2x + 3)2 a. y = In(2x + 3) +C b.y = (2x +…

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Q: (x² + 1) dx – 3x*y In y dy = 0

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Q: 1. (1– x)y' = y2 2. 2yy' — 2хуу' %3D у?

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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A: The given differential equation is tdvdt=v+t , t>0, At t=2, v=8. To Show:  When t=8, v=16(2+ln2).…

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Q: Your answer is correct. dy Write down a differential equation of the form dt all other solutions…

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Q: Its known that y, = y2(x) = are solutions for the differential equation x²y" – by = 0 the general…

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Q: 2. Determine the solution of differential equation de + Q=4 given that given that 10+2t dt Q(2)-…

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Q: Given: 1+ ce y = 1- ce 1+ ce y = 1- ce is a solution to the differential equation Show that dy 1 (ỷ…

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Q: Show that an implicit solution of 2x sin?(y) dx – (x² + 17) cos(y) dy = 0 is given by In(x2 + 17) +…

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Q: 2(у — х)dx + x(2у — х + 2)dy %3 0 Ans:2xyeУ — х?еУ %3D с | |

A: Differential equations

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Q: (10) Show that the solution of the differential equation y 4y +1Vy is y = r*(In V]r| + c)².

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Q: ) Prove that: (y -c} = C x is the solution of the differential equation dy dy 4x 2x dx 0= dx Then…

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Q: –7 + 12 d5x 7) 25 d*x -7- dt5 d²x + 12 dt3 + 8. = 0 dt4 dt2

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Q: 2. Verify that the indicated expression is a solution for the given differential Equation dy x3y3 –…

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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.