//solve diff-eq uing difference equations

//solve equations of the form ax^2 + bx + c = y
//this example solves x^2 + 2x + 4 = 0



public class diffeq
{
    
    public static void main ( String args[] )
    {
    
	//first find roots
	//X^2 + 2X + 4 = 0
	// (b+- sqrt ( b^2 -4ac ))/2a
	double a = 1;    
	double b = 2;
	double c = 4;
		
	
	if ( ( b*b-4*a*c )<0 ) {  //complex roots 
	    double r1_real = b/(2*a);
	    double r2_real = b/(2*a);
	    double r1_img = Math.sqrt ( (-1)*(b*b - 4*a*c) )/(2*a);
	    double r2_img = (-1) * (Math.sqrt ( (-1)*(b*b - 4*a*c) ))/(2*a);
	    double R1 = Math.sqrt( r1_real*r1_real + r1_img*r1_img );
	    double theta = Math.atan2( r1_img, r1_real );
	    System.out.println ( theta );
	    theta = theta*180/Math.PI;
	    System.out.println ( " y = " + R1 + "^n ( A cos (" + theta + "*n) + B sin (" + theta + "*n ) " );
	    
	}else{                   //real roots
	    double r1 = ( b + Math.sqrt( b*b - 4*a*c) )/( 2*a );
	    double r2 = ( b - Math.sqrt( b*b - 4*a*c) )/( 2*a );
	    
	    if ( r1 == r2 ) {
		System.out.println ( " y = " + r1 + "x^n  + " + r2 + "nx^n " );
	    }else{
		System.out.println ( " y = " + r1 + "x^n  + " + r2 + "x^n " );
	    }
	}
	
	
    }
    
}