What is the solution for y^'=(sqrt(x))/(e^y) ?

The solution for y^'=(sqrt(x))/(e^y) is y=ln(2/3 x^{3/2}+c_{1})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^'=(sqrt(x))/(e^y)

y^{^{'}} = \frac{x}{e ^{y}}

y = ln (\frac{2}{3} x^{\frac{3}{2}} + c_{1})

Solution steps

y^{'} (x) = \frac{x}{e ^{y}}

Solve separable ODE:

y = ln (\frac{2}{3} x^{\frac{3}{2}} + c_{1})

y = ln (\frac{2}{3} x^{\frac{3}{2}} + c_{1})

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

\frac{d y}{y} + (\frac{1}{x} + 1) d x = 0

3 x y^{^{'}} - 5 y = 0, y (1) = 2

\frac{d y}{d x} = - 6 x^{2} y + 9 x^{2}

y^{^{'}} tan (x) = a + y, y (\frac{π}{3}) = a

What is the solution for y^'=(sqrt(x))/(e^y) ?
The solution for y^'=(sqrt(x))/(e^y) is y=ln(2/3 x^{3/2}+c_{1})