What is the solution for (d^4+2d^2+1)y=0 ?

The solution for (d^4+2d^2+1)y=0 is y=c_{1}cos(x)+c_{2}sin(x)+x(c_{3}cos(x)+c_{4}sin(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^4+2d^2+1)y=0

(d^{4} + 2 d^{2} + 1) y = 0

y = c_{1} cos (x) + c_{2} sin (x) + x (c_{3} cos (x) + c_{4} sin (x))

Solution steps

(d^{4} + 2 d^{2} + 1) y = 0

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + x (c_{3} cos (x) + c_{4} sin (x))

y = c_{1} cos (x) + c_{2} sin (x) + x (c_{3} cos (x) + c_{4} sin (x))

\frac{d ^{3} y}{d x ^{3}} - \frac{d ^{2} y}{d x ^{2}} = 0

y^{^{'''}} - y^{^{''}} + 25 y^{^{'}} - 25 y = 0

y^{^{''}} - 16 y^{^{'}} - 63 y = 0

y^{^{''}} + \frac{3}{2} y^{^{'}} + \frac{3}{8} y = 0

5 \frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} - 90 y = 0

What is the solution for (d^4+2d^2+1)y=0 ?
The solution for (d^4+2d^2+1)y=0 is y=c_{1}cos(x)+c_{2}sin(x)+x(c_{3}cos(x)+c_{4}sin(x))