What is the solution for (dy)/(dx)= y/x+sqrt((y/x)^2-1) ?

The solution for (dy)/(dx)= y/x+sqrt((y/x)^2-1) is y= 1/(2e^{c_{1)}}+(e^{c_{1}}x^2)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)= y/x+sqrt((y/x)^2-1)

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

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

Solution steps

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

Solve using substitution:

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

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

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{1 + e ^{t}}

\int x 1 + x + \frac{x ^{2} + 4}{x - 1} d x

\frac{d}{d x} (x^{3} ln (x^{4} + 1))

\int_{2}^{x^{2}} cos (t^{2} + 1) d t

\frac{d}{d x} ((8 x - 1)^{2})

What is the solution for (dy)/(dx)= y/x+sqrt((y/x)^2-1) ?
The solution for (dy)/(dx)= y/x+sqrt((y/x)^2-1) is y= 1/(2e^{c_{1)}}+(e^{c_{1}}x^2)/2