What is the solution for y^{''}-2y^'+5y=2cos^2(2x) ?

The solution for y^{''}-2y^'+5y=2cos^2(2x) is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-2y^'+5y=2cos^2(2x)

y^{^{''}} - 2 y^{^{'}} + 5 y = 2 cos^{2} (2 x)

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + e^{x} cos (2 x) \cdot \int - \frac{cos ^{2} ( 2 x ) sin ( 2 x )}{e ^{x}} d x + e^{x} sin (2 x) (\frac{1}{6} cos^{5} (2 x) sin (2 x) + \frac{5}{6} (\frac{1}{4} cos^{3} (2 x) sin (2 x) + \frac{3}{8} (2 x + \frac{1}{2} sin (4 x))))

Solution steps

y^{''} (x) - 2 y^{'} (x) + 5 y = 2 cos^{2} (2 x)

Solve linear ODE:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + e^{x} cos (2 x) \cdot \int - \frac{cos ^{2} ( 2 x ) sin ( 2 x )}{e ^{x}} d x + e^{x} sin (2 x) (\frac{1}{6} cos^{5} (2 x) sin (2 x) + \frac{5}{6} (\frac{1}{4} cos^{3} (2 x) sin (2 x) + \frac{3}{8} (2 x + \frac{1}{2} sin (4 x))))

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + e^{x} cos (2 x) \cdot \int - \frac{cos ^{2} ( 2 x ) sin ( 2 x )}{e ^{x}} d x + e^{x} sin (2 x) (\frac{1}{6} cos^{5} (2 x) sin (2 x) + \frac{5}{6} (\frac{1}{4} cos^{3} (2 x) sin (2 x) + \frac{3}{8} (2 x + \frac{1}{2} sin (4 x))))

y^{^{''}} + 25 y = 3, y (0) = 1, y^{^{'}} (0) = 5

y^{^{''}} + 20 y^{^{'}} + 200 y = 400

y^{^{'''}} - 7 y^{^{''}} = x^{2} + 2 cos (x)

y^{^{''}} + y = tan^{2} (t)

y^{^{''''}} + 2 y^{^{''}} + y = 9 + cos (6 t)

What is the solution for y^{''}-2y^'+5y=2cos^2(2x) ?
The solution for y^{''}-2y^'+5y=2cos^2(2x) is