Answer to Question #230366 in Civil and Environmental Engineering for syra

Question #230366
Find the solution of the given differential equation and then find the particular solution for which a point (x,y) is given:

dy/dx = (2-x) (x+1); (x,y) = (-1,3)
1
Expert's answer
2021-08-28T06:16:17-0400

"y'\\:=\\left(2-x\\right)\\left(x+1\\right)\\\\\n\\mathrm{If\\quad }f'\\left(x\\right)=g\\left(x\\right)\\mathrm{\\quad then\\quad }f\\left(x\\right)=\\int g\\left(x\\right)dx\\\\\ny=\\int \\left(2-x\\right)\\left(x+1\\right)dx\\\\\ny=\\frac{x^2}{2}-\\frac{x^3}{3}+2x+c_1\\\\\ny=\\frac{x^2}{2}-\\frac{x^3}{3}+2x+\\frac{25}{6}"

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