What is the solution for (d^2y)/(dx^2)=4y,y(0)=0,y^'(0)=1 ?

The solution for (d^2y)/(dx^2)=4y,y(0)=0,y^'(0)=1 is y= 1/4 e^{2x}-1/4 e^{-2x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2y)/(dx^2)=4y,y(0)=0,y^'(0)=1

\frac{d ^{2} y}{d x ^{2}} = 4 y, y (0) = 0, y^{^{'}} (0) = 1

y = \frac{1}{4} e^{2 x} - \frac{1}{4} e^{- 2 x}

Solution steps

y^{''} (x) = 4 y

Solve linear ODE:

y = \frac{1}{4} e^{2 x} - \frac{1}{4} e^{- 2 x}

y = \frac{1}{4} e^{2 x} - \frac{1}{4} e^{- 2 x}

y^{^{''}} - y^{^{'}} = x e^{x}

12 = \frac{1}{( 22 \cdot 1 0 ^{- 6} )} y + \frac{33000 d y}{d x}

\frac{\partial}{\partial x} (ln (y) + 4 x)

x \to - 3 lim (\frac{16 - x ^{\frac{4}{3}}}{4 - x ^{\frac{2}{3}}})

x \to 3 - lim (\frac{1}{3 - x})

What is the solution for (d^2y)/(dx^2)=4y,y(0)=0,y^'(0)=1 ?
The solution for (d^2y)/(dx^2)=4y,y(0)=0,y^'(0)=1 is y= 1/4 e^{2x}-1/4 e^{-2x}