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- Find a solution: ty''-ty'+y=2; y(0)=2,y'(0)=-1Write the given second order equation as its equivalent system of first order equations. u" + 4.5u' – 7.5u = -7 sin(3t), u(1) = -7.5, u'(1) = -6 Use v to represent the "velocity function", i.e. v = u'(t). Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) u' = %3D Now write the system using matrices: u d + dt V V and the initial value for the vector valued function is: u(1) v(1)Determine all solutions y' = (x-y + 3)²
- Find a particular solution to the given higher-order equation. y''' - y'"' - 22y' + 40y = - 40t² +244t-268 A particular solution is yp (t) = .7 b) For the system, 6 - 1 Y': Y 5 4 Write the natural period of the oscillations, round the answer to three digits after the decimal signFind the general solution of the equation, y'x'(1- y). a. y= Ce +1 b. y = Cei +1 c y- Ce+1 d. y= Ce+1