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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d x}{d t} = 60 - \frac{x}{100}, x = 2000, t = 0

x y^{2} cos (x) d x - 3 x^{2} y cos (x) d y = 0

\frac{d y}{d x} - y (6 x + 1) = 0

y^{^{'}} = x y - 8 x, y (0) = 9

7 y d x = - 3 x d y

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