What is the solution for 1/y (dy)/(dx)=e^x+log_{e}(y) ?

The solution for 1/y (dy)/(dx)=e^x+log_{e}(y) is y=e^{c_{1}e^x+xe^x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

1/y (dy)/(dx)=e^x+log_{e}(y)

\frac{1}{y} \frac{d y}{d x} = e^{x} + lo g_{e} (y)

y = e^{c_{1} e^{x} + x e^{x}}

Solution steps

\frac{1}{y} \frac{d y}{d x} = e^{x} + lo g_{e} (y)

Solve exact ODE:

y = e^{c_{1} e^{x} + x e^{x}}

y = e^{c_{1} e^{x} + x e^{x}}

What is the solution for 1/y (dy)/(dx)=e^x+log_{e}(y) ?
The solution for 1/y (dy)/(dx)=e^x+log_{e}(y) is y=e^{c_{1}e^x+xe^x}