MATH237 Lecture 53: MATH237 Lecture Notes 53

ODE with Non-constant Coefficients (a) Find the general solution of r2y" - ry 4y) (b) Prove that yı = er2 and y2 = y"-4ry' + (47-2)y = 0, and re are solutions of and write the general solution. Solve it with the initial conditions y(1) -

(1 point) Use the change of variables s ry, t ry to compute Jn y2 dA, where R is the region bounded by ry-1, ry 6, y21, zy6.

MATH 227 14 pts 8 Find the volume of the solid under the surface z = ry and above the triangle in the ry-plane with vertices (1.0), (2,1), and (4.0)