Verify that the function y(r) = 2, is a solution of the initial value problem dy + 2y = 3y, v(0) =; dr Find the largest interval of this solution. Is it a unique solution? Justify your answer using a theorem from section 1.2.

Q: Find all solutions to (2cos x+ V3)(2sinx-1)=0

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A: The function y(x)=ce-2x+e-x. is solution of equation y'+2y=e-x Linear first order differential…

Q: 4. Suppose the following functions are a general solution of: y(4) + a3y/" + azy" + a;y' + a0y = 0

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Q: x' +(log3 3)x – v2 = 0

A: Note: If a polynomial gives one solution in complex number then conjugate of this solution must be…

Q: My last digit of student number is 4.

A: Step 1:Step 2:Step 3:Step 4:Step 5:Step 6:Step 7:Step 8:Step 9:Step 10:

Q: Can you elaborate how to incorporate c into the solution. Like c=0? And how does f'(0)=7 and…

A: Solution below

Q: tions. Find the General solution of y" - 2y' + 5y = 4tet with Real valued func-

A: We have to find the general solution of the differential equation.

Q: 6. Find the tangent line equations for the given functions at the given point(s): x2 + 3xy + y3 = 15…

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Q: Solve the equation 2 x " y " + 3 x y = (1 + x ) y = ху - which has a regular singula Point x = 0.…

A: Here both p(x)=32xand q(x)=−1+x2x2 aree non analytic at x=0 so 0 is a singular point. But both…

Q: 1. By applying an appropriate theorem, explain why x-100 x = 0 has a solution in the interval (1,4).

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Q: b) x²y + xy = 1 x>0 y(1) = 2

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Q: 3. Find all solutions to the equation (D² – 3D + 2)y(x) = 2e3ª.

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Q: Discuss the maximum and minimum of x?+y'+6x+12.

A: Given: x2+y2+6x+12