What is the solution for (dy)/(dx)=e^{(6x-3y)},y(0)=3 ?

The solution for (dy)/(dx)=e^{(6x-3y)},y(0)=3 is y=(ln(1/2 e^{6x}+e^9-1/2))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=e^{(6x-3y)},y(0)=3

\frac{d y}{d x} = e^{(6 x - 3 y)}, y (0) = 3

y = \frac{ln ( \frac{1}{2} e ^{6 x} + e ^{9} - \frac{1}{2} )}{3}

Solution steps

\frac{d y}{d x} = e^{(6 x - 3 y)}

Solve separable ODE:

y = \frac{ln ( \frac{1}{2} e ^{6 x} + e ^{9} - \frac{1}{2} )}{3}

y = \frac{ln ( \frac{1}{2} e ^{6 x} + e ^{9} - \frac{1}{2} )}{3}

\int (2 - e^{x})^{2} d x

f (x) = x^{2} (1 - 5 x)

\int \frac{30}{( 225 x ^{2} + 1 ) ^{2}} d x

\frac{10}{( 1 + e ^{- x} )}

\frac{\partial}{\partial x} (e^{\frac{2}{x}})

What is the solution for (dy)/(dx)=e^{(6x-3y)},y(0)=3 ?
The solution for (dy)/(dx)=e^{(6x-3y)},y(0)=3 is y=(ln(1/2 e^{6x}+e^9-1/2))/3