(h) How many arbitrary constants are there in the solution of `y'''+y''+3y'+5y=0` `(1, 2, 3, 4)`

In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it. (1) 2x+3y=7 , 6x+5y=11 (2) 6x+5y=11 , 9x+(15)/2y=21 (3) -3x+4y=5 , 9/2x-6y+(15)/2=0

Solution of differential equation (dy)/(dx)=(y^2-2x y-x^2)/(y^2+2x y-x^2) is x^2-y^2+c(x-y)=0 (c is arbitrary constant) x^2+y^2+c(x+y)=0 (c is arbitrary constant) a straight line if it passes through (1,-1) a circle if it passes through (1, 1)

The differential equation which represents the family of curves y""=""c_1e^(c_2x) , where c_1"and"c_2 are arbitrary constants, is (1) y '=""y^2 (2) y ' '=""y ' y (3) y y ' '=""y ' (4) y y ' '=""(y ')^2

y=x^2 + 3x-7 y-5x+8=0 How many solutions are there to the system of equations above?

If the solution of the differential equation (1+e^((x)/(y)))dx+e^((x)/(y))(1-(x)/(y))dy=0 is x+kye^((x)/(y))=C (where, C is an arbitrary constant), then the value of k is equal to

Verify that y = e^(-2x) is a solution of the differential equation y''' + 4y'' + 3y' - 2y = 0 .

The angle between the regression lines: x-2y+3=0, 4x-5y+1=0 is

The solution of the differential equation y_1y_3=y_2^2 is

(y^(2)+ky-3)(y-4)=y^(3)+by^(2)+5y+12 In the equation above, k is a nonzero constant. If the equation is true for all values of y, what is the value of k?

If X and Y are 2xx2 matrices, then solve the following matrix equations for X and Y 2X+3Y=[[2,3],[4,0]],3X+2Y=[[-2,2],[1,-5]]