What is the solution for (dy)/(dx)=(1+e^{x^2})(5+x) ?

The solution for (dy)/(dx)=(1+e^{x^2})(5+x) is y=5x+(x^2)/2+(5sqrt(pi))/2 \erfi(x)+1/2 e^{x^2}+c_{1}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=(1+e^{x^2})(5+x)

\frac{d y}{d x} = (1 + e^{x^{2}}) (5 + x)

y = 5 x + \frac{x ^{2}}{2} + \frac{5 π}{2} erfi (x) + \frac{1}{2} e^{x^{2}} + c_{1}

Solution steps

\frac{d y}{d x} = (1 + e^{x^{2}}) (5 + x)

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = (1 + e^{x^{2}}) (5 + x)

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

then

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

y = \int (1 + e^{x^{2}}) (5 + x) d x

\int (1 + e^{x^{2}}) (5 + x) d x = 5 x + \frac{x ^{2}}{2} + 5 \cdot \frac{π}{2} erfi (x) + \frac{1}{2} e^{x^{2}} + c_{1}

y = 5 x + \frac{x ^{2}}{2} + 5 \cdot \frac{π}{2} erfi (x) + \frac{1}{2} e^{x^{2}} + c_{1}

Simplify

y = 5 x + \frac{x ^{2}}{2} + \frac{5 π}{2} erfi (x) + \frac{1}{2} e^{x^{2}} + c_{1}

\frac{4}{cos ( x )} + \frac{1}{tan ( x )}

\frac{d}{d x} (x e^{(- x^{2})})

\frac{( 4 x ^{2} + 8 x + 2 )}{x}

y^{^{'}} + 175 x = 0, y (2) = 0

\frac{d y}{d t} = 4 y + y^{3}, y (0) = 1

What is the solution for (dy)/(dx)=(1+e^{x^2})(5+x) ?
The solution for (dy)/(dx)=(1+e^{x^2})(5+x) is y=5x+(x^2)/2+(5sqrt(pi))/2 \erfi(x)+1/2 e^{x^2}+c_{1}