MAT244H1 Study Guide - Midterm Guide: Wronskian

• School: UTSG
• Department: Mathematics
• Course: MAT244H1
• Professor: All

Document Summary

Number of test pages: (including this cover sheet) Page 2 of 9: (10 points) variation of parameters (you can just use formulas for u1 and u2 here without deriving them. The next question is about the derivation of the formulas for u1 and u2. ) Solve the following initial value problem y(cid:48)(cid:48) + 3y(cid:48) 10y = 7tet, y(0) = 35. Page 4 of 9: (3 points) variation of parameters. For an inhomogeneous second order linear ode y(cid:48)(cid:48) + p(t)y(cid:48) + q(t)y = g(t), (1) Nding a solution using variation of parameters means nding functions u1 and u2 so that y1u1 + y2u2 is a solution of (1), where y1 and y2 are solutions of the homogeneous version of (1). In the derivation we obtain the two equations y1u(cid:48) Use these two equations to get the nal formulas for u1 and u2 (that express u1 and u2 as integrals involving g, the wronskian of y1, y2 and y1, y2 themselves. )