Question: Show the COMPLETE solution to the following problem. Box the conclusion or final answer to the problems. 1. Verify that y = de * +

Show the COMPLETE solution to the following problem. Box the conclusion or final answer to the problems. 1. Verify that y = de * + be""+ex is a solution to the equation: y + 3y + 2y =12exx. 2. Verify that y = Inin [coscos (x - a) ] + b is a solution to the equation: y + () ) +1=0. 3. Find all values of m for which y = m(e -x?)" is a solution of x duty dy =0 in the interval (-e, e). 4. Find all values of y = x" is a solution of 3xy - xy + 2xy -2y =0 in the interval (- 00, 03). 5. Solve (2x + 3y) dx+ (y -x) dy = 0. Use the method of homogeneous equations. 6. Find the particular solution of the following IVP: ( yvr + yz) dx + ( xxx + yz ) dy = 0 x = 3, y=4 7. Find the primitive solution to the following DE. Use the appropriate method of solution. (year + 4x ) dx + (2xyet - 312 ) chy = 0 8. Find the primitive solution to the following DE. Use the transformation xy = v. (v-x)dx - (x+xy)dy =0

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