What is the solution for y^'=0.1ln((4000)/y)y,y(0)=500 ?

The solution for y^'=0.1ln((4000)/y)y,y(0)=500 is y=125*2^{5-3e^{-t/(10)}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^'=0.1ln((4000)/y)y,y(0)=500

y^{^{'}} = 0.1 ln (\frac{4000}{y}) y, y (0) = 500

y = 125 \cdot 2^{5 - 3 e^{- \frac{t}{10}}}

Solution steps

y^{'} (t) = 0.1 ln (\frac{4000}{y}) y

Solve separable ODE:

y = 125 \cdot 2^{5 - 3 e^{- \frac{t}{10}}}

y = 125 \cdot 2^{5 - 3 e^{- \frac{t}{10}}}

\frac{d}{d x} (6 π x^{2})

\frac{d}{d x} (e^{\frac{x}{5}})

\frac{d}{d x} ((2 x + 1)^{5})

\int_{1}^{t} 35 x^{- 3} d x

\int \frac{x ^{3}}{3 ( x ^{2} + 1 )} d x

What is the solution for y^'=0.1ln((4000)/y)y,y(0)=500 ?
The solution for y^'=0.1ln((4000)/y)y,y(0)=500 is y=125*2^{5-3e^{-t/(10)}}