use elimination to solve each system of differential equatio

use elimination to solve each system of differential equations 2x\' +y\'=-x ; x\'+y\'=x

Solution

Given 2x^l + y^l = -x ............(1)

x^l +  y^l = x .............(2)

ie , x^l +( x^l +  y^l) = -x

  x^l + x = -x

  x^l = -2x

integrating , x = -x² +C

Now Substituting the value of x in eqn (2)

-x² + y^l = x

ie , y^l = x + x²

Integrating , y = x²/2 + x³/3 +C

So the solution of the system is  x = -x² +C and  y = x²/2 + x³/3 +C