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provide detailed solutions
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answerhappygod
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provide detailed solutions
provide detailed solutions
Question 1 [20 pts]: a) [5 pts]: Verify that the differential equation is exact: (5x4 sin(y)+9x8y8 )dx+(x5 cos(y)+8x²y7)dy = 0. b) [15 pts]: Find the general solution to the above differential equation. Question 2 [20 pts]: a) [15 pts]: Solve the following linear system in detailed, by using Gauss-Jordan elimination: x+y+z = 4 4xyz = 3 3x = y + z = 1 b) [5 pts] Is the system homogeneous and consistent? What about the solution type ? Is it unique ? Question 3 [20 pts]: Let -2x+6y=k²7k- 8 6x - 2y = k²9k +8 be a system of equations. a) [5 pts]: If the system is homogeneous, what is the value(s) for k ? b) [15 pts]: Solve the homogeneous system. Is the solution trivial? Is the solution unique ?
Question 1 [20 pts]: a) [5 pts]: Verify that the differential equation is exact: (5x4 sin(y)+9x8y8 )dx+(x5 cos(y)+8x²y7)dy = 0. b) [15 pts]: Find the general solution to the above differential equation. Question 2 [20 pts]: a) [15 pts]: Solve the following linear system in detailed, by using Gauss-Jordan elimination: x+y+z = 4 4xyz = 3 3x = y + z = 1 b) [5 pts] Is the system homogeneous and consistent? What about the solution type ? Is it unique ? Question 3 [20 pts]: Let -2x+6y=k²7k- 8 6x - 2y = k²9k +8 be a system of equations. a) [5 pts]: If the system is homogeneous, what is the value(s) for k ? b) [15 pts]: Solve the homogeneous system. Is the solution trivial? Is the solution unique ?