What is the solution for f(x)= 1/(1+x^2)f^'(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

f(x)= 1/(1+x^2)f^'(x)

f (x) = \frac{1}{1 + x ^{2}} f^{^{'}} (x)

f (x) = e^{x + \frac{x ^{3}}{3} + c_{1}}

Solution steps

f (x) = \frac{1}{1 + x ^{2}} f^{'} (x)

Solve separable ODE:

f (x) = e^{x + \frac{x ^{3}}{3} + c_{1}}

f (x) = e^{x + \frac{x ^{3}}{3} + c_{1}}

\frac{d y}{d x} = 7 x sec (y)

\frac{d y}{d x} y = tan (3 x^{4})

\frac{d y}{d x} = x^{5} (y - 2), y (0) = 6

y^{^{'}} + tan (2 \cdot x) y = 0, y (0) = 5

V^{^{'}} = 4 kπ (\frac{3}{4 π})^{\frac{2}{3}} V^{\frac{2}{3}}

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