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Formulate a differential equation whose general solution is z(t)=A sin t-B cos t.
d²y/dx²+dy/dx+2y=0
y'y'''-(y'')^2=(y'')^3
A particle is attached to the lower end of a spring, the upper end of which oscillates about a point O. The motion of the particle can be modelled by the equation
d^2x/dt^2 + 25x = 0.5sint.
where x is the displacement of the particle from its equilibrium point. When t = 0, x = 0 and the particle is at rest.
(a) Solve this differential equation to find x in terms of t and describe briefly the motion of the particle.
In order to damp the oscillations the particle is submerged in liquid and the motion of the particle can be modelled as
d^2x/dt^2 + kdx/dt + 25x = 0.5sint, where k is a constant.
(b) Explain why k must be positive. Give the range of values of k for which the system will be underdamped.
d²y/d²x+2dy/dx+10y=0
solve dx/2x(y+z^2) = dy/y(2y+z^2) = dz/z^3
(x-y)p-(x-y+z)q=z
Give the general solution using determination of
Integrating Factors.
1. (x^2 + y^2 + 1)dx + x(x − 2y)dy = 0
2. y(4x + y)dx − 2((x^2 − y)dy = 0
3. y(y + 2x − 2)dx − 2(x + y)dy = 0
4. y(8x − 9y)dx − 2x(x − 3y)dy = 0
5. y(2x^2 − xy)dx − (x − y)dy = 0
6. 2(2y^2 + 5xy − 2y + 4)dx + x(2x + 2y − 1)dy = 0
7. (2x^2 + 3xy − 2y + 6x)dx + x(x + 2y − 1)dy = 0
2e^-x + e^y = 3^x-y at 0,0
v=11sin4t-5cos5t
