(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

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 .

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?

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

Solve the following pair of linear equations by the substitution method. (i) x+y=14 ;x- y=4 (ii) s-t=3; s/3+t/2=6 (iii) 3x-y=3;9x-3y=9 (iv) 0. 2 x+0. 3 y=1. 3 ;0. 4 x+0. 5 y=2. 3 (v) sqrt(2)x+sqrt(3)y=0;sqrt(3)x-sqrt(8)y=0 (vi) 3x/2-5y/2=-2;x/3+y/2=13/6

(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]]