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- utilize the characteristic equations method to solve the equation y''-5y'+3y=0 y(0)=3, y'(0)=-1Find two linearly independent solutions of 2x2y"-xy'+(-6x+1)y=0, x>0 of the forma. Draw a direction field and sketch a few trajectories. b.Express the general solution of the given system of equations in terms of real-valued functions. c.Describe the behavior of the solutions as t → ∞.4.x′=(12−5−1)x
- Find two linearly independent solutions of y''+2xy = 0 of the form in the imagea. Draw a direction field and sketch a few trajectories. b.Express the general solution of the given system of equations in terms of real-valued functions. c.Describe the behavior of the solutions as t → ∞. 3.x′=(1−15−3)xUse cramer's rule to solve this simultaneous equation a){4x-3y=2} {3x+y=-1}