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}

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(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}

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}