Test review for Differential equations

Please show all possible work if you want any possibility of credit. H 4 1s Consider the ODE y" - y' - 2y = 3e2t. The complementary solution is yc(x) = Cle2 + Cze . Use the . H: Calculators / Computer Algebra Systems are not allowed except, possibly, GRADE method of undetermined coefficients (superposition method) to find the particular solution. the MATH D FRAC button or to check your work. You must use exact answers . . T: Use calculators / Computer Algebra Systems to your heart's content. For of 50 something more complicated than evaluation of a function, show your work! Round answers (where appropriate) to 4 places after the decimal. H 1 10 Consider the functions y1 (x) = cos(5x) and yz(x) = x cos(5x). Assume they are solutions to some ODE. Use the Wronskian to determine whether or not the functions are linearly independent . Differential Equations - Higher Order ODE Take Home TANIA TATTSTTT Linearly Independent Linearly Dependent H 2 pes Consider the polynomial p()) = 16+ 15+ 14+ 13 + 12 + A -1. Use Descarte's Rule of Signs to determine Use variation of parameters to solve y" ty = sec? (x). the possible numbers of positive real roots, negative real roots, and complex roots. List the possibilities separated by commas. No, don't find the roots, just list the possibilities. ATTTOTT ANDT ATMA Positive Real Negative Real Complex H 3 pts Suppose the characteristic equation of a homogeneous ODE is roots * =0, 0, 0, 2, -2, -3+52 Write down the solution