What is the solution for (dy)/(dx)=4(x^2+1),x(pi/4)=1 ?

The solution for (dy)/(dx)=4(x^2+1),x(pi/4)=1 is y=4((x^3)/3+x)+c_{1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=4(x^2+1),x(pi/4)=1

\frac{d y}{d x} = 4 (x^{2} + 1), x (\frac{π}{4}) = 1

y = 4 (\frac{x ^{3}}{3} + x) + c_{1}

Solution steps

\frac{d y}{d x} = 4 (x^{2} + 1)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = 4 (x^{2} + 1)

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int 4 (x^{2} + 1) d x

\int 4 (x^{2} + 1) d x = 4 (\frac{x ^{3}}{3} + x) + c_{1}

y = 4 (\frac{x ^{3}}{3} + x) + c_{1}

\int (8 x^{3} + \frac{1}{x ^{2}}) d x

y = 2^{- x}, (- 1, 2)

\frac{d}{d x} (1 - 4 cos (x))

\int_{- 2}^{2} \frac{1}{x ^{2} - 9} d x

\int tan^{4} (x se) c^{2} x d x

What is the solution for (dy)/(dx)=4(x^2+1),x(pi/4)=1 ?
The solution for (dy)/(dx)=4(x^2+1),x(pi/4)=1 is y=4((x^3)/3+x)+c_{1}