Solve the following problems а) ди ди = 1 + u, + 3x- dx t > 0, -o < x < ∞, dt u(x, 0) = f(x).

Q: You are buying a car. Would you prefer a higher rate for a lower term or a lower rate for a longel…

A: Given that You are buying a car. Would you prefer a higher rate for a lower term or a lower rate for…

Q: find the a general solution to dy/dt = {{-9,12},{6,-8}}y

A: (.)  Given ,            (.)  Consider a system of differential equation ,…

Q: (a) Determine all critical points of the given system of equations. (b) Find the corresponding…

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Q: - y" 3y'+2y=- 1+ e-x Use Variation of Parameters. Do not simplify final result.

A: Step 1: Step 2: Step 3: Step 4:

Q: the st sub: Z = the + 4x = x²(4t + 3), x(1) = 4.

A: Given differential equationAssume

Q: 2. で-5e dt = 4.

A: ∫xndx = xn+1n+1

Q: b. Determine whether the statement is true or false and justify your answer. Determine which of the…

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Q: + y = ty dt

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Q: show that the solution y(t)=e^2tsin(t) is linearly independant.

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Q: 2. Find all solutions: dt dy dx = 4x + y x + 4y' x > 0.

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Q: Find the general solution to the following Bernoulli Equation: dy/dt - 3 * sqrt(t) * y = sqrt( t *…

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Q: Show that y = e^2t is a solution of y’’’ - 2y’ - 4y = 0 (where ‘ denotes d/dt), and find the general…

A: We need to solve differential equation and show that y = e^2t is a solution.

Q: solve  utt- 4uxx=x2          -infinity 0  subject to initial conditions: u(x,0) = x  ut(x,0)=0

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Q: b) xy'+ 2y = 3x

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Q: (D2 +DD'+D'-1) z = 0

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