6) (a). (8pts) Find a particular solution to y" – 2y' + y = 24e'. Hint: Use the method of undetermined coefficients. (Calculate the coefficients) (b). (4pts) Find the form of a particular solution to 0"(t) + 20'(t) + 40(t) = 7e2 cosv3t COSV %3D Hint: Use the method of undetermined coefficients (Do not evaluate coefficients).

Q: Solve the initial value problem. * = et sin (et - 4), y(ln 4) = 0 %3D O A) y = -cos (et - 4) + 1 %3D…

A: Given:-   D.E:dydt=et sm et -4                  Initial condition: y ln 4=0   To calculate:…

Q: Find the general solution. Please make the solution steps clear.

A:

Q: 5.) 4 cubic equation Cdegree 3 palynomial) . y aoes thidugh the Sbints points 2,0,5),(2,9) and…

A: The given points are -2,1,0,5,2,9 and 3,36. The general form of the cubic equation is…

Q: The equation y" + y' +cos (t) y = e" (9 – t) can be solved by O a) Undetermined coefficients O b)…

A:

Q: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: Find all solutions to the equation: csc²(x) - 6cot(x) = -4.

A:

Q: C1e + C2e* . These are The solution of y" – 2y' 15y = 0 is y the values of C, and C2 if y (0) = 11…

A:

Q: Using variation of parameters, find the general solution to the given DE. 1 4 csc (3x) General…

A:

Q: Use the method of undetermined coefficients to find one solution of y" − 6y' + 35y = 16e³t cos(5t) +…

A:

Q: Q6. Use the method of Variation of parameters to solve (i) y" + y = tan x. (ii) x²y"+xy'+(x² – })y =…

A: Hint: particular solution of a differential equation from method of variation of parameters suppose…

Q: 3. (4.2 #3) Find the general solution. y" + 8y + 7y=0

A: The given equation is; y''+8y'+7y=0

Q: Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,511.9 miles. The…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.