SOLUTION: In the following differential equation, test for exactness and determine the solution: {{{ (xdy-ydx)/y^2=x^3dx }}} Answer: {{{ 4x+x^4y=Cy }}}

Algebra ->  Expressions -> SOLUTION: In the following differential equation, test for exactness and determine the solution: {{{ (xdy-ydx)/y^2=x^3dx }}} Answer: {{{ 4x+x^4y=Cy }}}      Log On


   

Question 1196937: In the following differential equation, test for exactness and determine the solution:
+%28xdy-ydx%29%2Fy%5E2=x%5E3dx+
Answer: +4x%2Bx%5E4y=Cy+
Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.

%28xdy-ydx%29%2Fy%5E2 = x%5E3dx


Left side is  d%28-%28x%2Fy%29%29.


Right side is  d%28%281%2F4%29%2Ax%5E4%29.


So, your equation is

    d%28-%28x%2Fy%29%29 = d%28%281%2F4%29%2Ax%5E4%29.


It implies

    -%28x%2Fy%29 = %281%2F4%29x%5E4 + C,    where  C = const.


It means that 

    4x + x^4*y = Cy.


which is your answer.

Solved.