What is the solution for y^{''}+4pi^2y=cos^3(2pix),y(10)=2 ?

The solution for y^{''}+4pi^2y=cos^3(2pix),y(10)=2 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+4pi^2y=cos^3(2pix),y(10)=2

y^{^{''}} + 4 π^{2} y = cos^{3} (2 π x), y (10) = 2

y = (2 - \frac{1}{16 π ^{2}}) cos (2 π x) + c_{2} sin (2 π x) + \frac{1}{16 π ^{2}} cos^{5} (2 π x) + \frac{1}{4 π ^{2}} sin (2 π x) (cos^{3} (2 π x) sin (2 π x) + \frac{3}{8} (2 π x - \frac{1}{4} sin (8 π x)))

Solution steps

y^{''} (x) + 4 π^{2} y = cos^{3} (2 π x)

Solve linear ODE:

y = (2 - \frac{1}{16 π ^{2}}) cos (2 π x) + c_{2} sin (2 π x) + \frac{1}{16 π ^{2}} cos^{5} (2 π x) + \frac{1}{4 π ^{2}} sin (2 π x) (cos^{3} (2 π x) sin (2 π x) + \frac{3}{8} (2 π x - \frac{1}{4} sin (8 π x)))

y = (2 - \frac{1}{16 π ^{2}}) cos (2 π x) + c_{2} sin (2 π x) + \frac{1}{16 π ^{2}} cos^{5} (2 π x) + \frac{1}{4 π ^{2}} sin (2 π x) (cos^{3} (2 π x) sin (2 π x) + \frac{3}{8} (2 π x - \frac{1}{4} sin (8 π x)))

y^{2} = x + 1, x = 3

x \to 2 - lim (\frac{x - 3}{x + 2})

\int (4 t^{3}) d t

f (x) = \frac{1}{x} + \frac{1}{1 - x}

\int \frac{x ^{3}}{( 5 x + 2 ) ^{3}} d x

What is the solution for y^{''}+4pi^2y=cos^3(2pix),y(10)=2 ?
The solution for y^{''}+4pi^2y=cos^3(2pix),y(10)=2 is