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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = sin (ln (x) + c_{1}) x

Solution steps

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

Solve using substitution:

y = sin (ln (x) + c_{1}) x

y = sin (ln (x) + c_{1}) x

x (x + 5 y) (\frac{d y}{d x}) + (y (3 x + 5 y)) = 0

\int (\frac{1}{sin ( x )}) d x

(x + 2)^{2} + (y - 3)^{2} = 37, (- 8, 2)

f (x) = x^{3} + 2 x, at x = - 1

\frac{d}{d x} (\frac{1 + x}{1 - x})

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