What is the solution for (dy)/(dx)=e^{-x^2},y(3)=5 ?

The solution for (dy)/(dx)=e^{-x^2},y(3)=5 is y=(sqrt(pi))/2 \erf(x)+5-(0.99997…sqrt(pi))/2

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(dy)/(dx)=e^{-x^2},y(3)=5

\frac{d y}{d x} = e^{- x^{2}}, y (3) = 5

y = \frac{π}{2} erf (x) + 5 - \frac{0.99997 \dots π}{2}

Solution steps

\frac{d y}{d x} = e^{- x^{2}}

Substitute

\frac{d y}{d x}

with

y^{'} (x)

y^{^{'}} (x) = e^{- x^{2}}

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

then

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

y = \int e^{- x^{2}} d x

\int e^{- x^{2}} d x = \frac{π}{2} erf (x) + c_{1}

y = \frac{π}{2} erf (x) + c_{1}

Apply initial conditions:

y = \frac{π}{2} erf (x) + 5 - \frac{0.99997 \dots π}{2}

y = \frac{π}{2} erf (x) + 5 - \frac{0.99997 \dots π}{2}

\int (4 - 3 x)^{5} + e^{2 x + 5} + sin (9 x) d x

y^{^{'}} + \frac{y}{x} = x

\int_{1}^{\infty} \frac{3}{x ^{5}} d x

\frac{d}{d y} (2 x y^{2} - 3)

t^{4}

What is the solution for (dy)/(dx)=e^{-x^2},y(3)=5 ?
The solution for (dy)/(dx)=e^{-x^2},y(3)=5 is y=(sqrt(pi))/2 \erf(x)+5-(0.99997…sqrt(pi))/2