Question

I need a help. Resolve the questions:
a. (x^2 – y^2) dx + 2xydy = 0

b. y’ + (1/x)y = ex^2

c. y’’ + 2y’ + 2y = 0

d. y’’ – 3y’ + 2y = sen x

e. (By Laplace transform)

y’’ – y = 0, y(0) = 1, y’(0) = 1

f. { x’ = y

{y’ = -2x +3y

g. (by power series) y’ = y
Usar a derivação termo a termo das séries

2. show that the series converges

∑ =1/n^2 when n=1
and tends to infinity

converge

Answer 1

\[\sum_{n=1}^{\infty} = 1/n^2\] converges