What is the solution for (dy)/(dt)=0.06y+3000,y(0)=30000 ?

The solution for (dy)/(dt)=0.06y+3000,y(0)=30000 is y=(e^{0.06t+8.47637…})/(0.06)-(3000)/(0.06)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dt)=0.06y+3000,y(0)=30000

\frac{d y}{d t} = 0.06 y + 3000, y (0) = 30000

y = \frac{e ^{0.06 t + 8.47637 \dots}}{0.06} - \frac{3000}{0.06}

Solution steps

\frac{d y}{d t} = 0.06 y + 3000

Solve separable ODE:

y = \frac{e ^{0.06 t + 8.47637 \dots}}{0.06} - \frac{3000}{0.06}

y = \frac{e ^{0.06 t + 8.47637 \dots}}{0.06} - \frac{3000}{0.06}

\frac{d x}{d t} = 100 - \frac{x}{100}, x (0) = 2000

\frac{d y}{d x} = \frac{x ^{3}}{( y + 1 )}

y^{^{'}} = \frac{x ( 1 + y )}{y ( x + 2 )}

y^{^{'}} = 3 x (1 - y)

\frac{d y}{d x} = 3 x^{2} y, y = 2, x = 3

What is the solution for (dy)/(dt)=0.06y+3000,y(0)=30000 ?
The solution for (dy)/(dt)=0.06y+3000,y(0)=30000 is y=(e^{0.06t+8.47637…})/(0.06)-(3000)/(0.06)