Question

dy/dx=1+x solve by differential equation

Answer 1

y' = 1+x
y = x + (1/2)x^2 + C

Does that fit?

Answer 2

\[y(x) = c_1+1/2 x (x+2)\]

Answer 3

y = x[(x/2)+1] + C ??

Answer 4

\[dy = \left( x + 1 \right)dx\]
\[\int\limits_{}{dy}=\int\limits_{}(x+1){dx}\]
\[y= (1/2) x^2 + x + C\]