1. Consider the ODE y" + 3y' + 2y = te-4t. (a) Find the general solution, y(t), to the associated homogeneous equation. (b) Using the method of undetermined coefficients, find the particular solution, yp(t), to the above equation. (c) If y(0) = 1 and y' (0) = 1, find the unique solution to the equation above.

Q: determine the equation of this parabola

A: The general form of the parabola is y=ax-h2+k where h,k is the vertex of the parabola.

Q: 2k, {}) 4k

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Q: 22) Does the point D(7.-1, 8) lie on the line with symmetric equations - 4 2-69 *3=1+2=20? Explain.

A: To check if the point  D(7, -1, 8)  lies on the line with symmetric equations 3x−4​=1y+2​=2z−6​, we…

Q: a) What is the equation of a straight line that passes through (2,0) and has a gradient of -3 ? b)…

A: a) The given data is: x1,y1=2,0m=-3 To find the equation of the straight line.

Q: 3 ation 4x² - yz + 4z³ - 25 = 0 at the point (1,25,-1).

A:

Q: Find 3 different homogeneous coordinate representations for the Cartesian point (1,-2)

A:

Q: Number 8

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Q: FIND THE VERTEX USING X=-B/2A, THEN USE TABLE OF VALUES AND FIND 4 OTHER POINTS FOR A PARABOLA…

A: (a) y=x2+2x-4 We know that the vertex of the parabola y=ax2+bx+c is -b2a,y Therefore comparing the…

Q: Solve the IVP y" – 8y' + 25y = 0; y(0) = 2, y'(0) = 2

A:

Q: y -1 Q2) L, =Xx2 = -1 - 2 Fand equation of plane Canternng them

A:

Q: (a) Show that Sin z = 0 if and only if z=kπ, k=0₁ ± (b) show that isin l = sinx + sinh y, exty 2 2

A: Value of the modulus of sinz

Q: Parabola y 41 Find clocest pounts Du parebole to (1,0) (1,0) セニX マ よっ(笑が+ Take denivate Set equal to…

A: To find the point on the parabola that is closest to (1,0) You have done the correct setup , you can…

Q: z is a complex variable z=x+iyFind all points of discontinuityf(z)=(3z^2 +4)/(z^4 -16)

A: To locate the points of discontinuity of the given function f(z) of the complex variable z.