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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = tan (- 1 - x^{2} + c_{1})

Solution steps

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

Solve separable ODE:

y = tan (- 1 - x^{2} + c_{1})

y = tan (- 1 - x^{2} + c_{1})

\frac{d y}{d x} = x^{3} y + 3 x^{3}

y^{^{'}} = - x^{2} y

\frac{d y}{d x} = - 5 y, y = 7, x = 0

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

x \frac{d y}{d x} = e^{7 y + x}, x > 0

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