Show that (3,4) and (0,6) are the solutions of the equation 2x+3y=18

Show that the function y=(A+B x)e^(3x) is a solution of the equation (d^2y)/(dx^2)-6(dy)/(dx)+9y=0.

Show that x=2,\ \ y=1 and x=4,\ \ y=4 are solutions of the system of equations: 3x-2y=4;\ \ \ 6x-4y=8 .

Write two solutions of the following are solutions of the equation 2x-y=6\ and which are not: (3,\ 0) (ii) (0,\ -6) (iii) (2,\ -2)

Show that y=e^(2x) is a solution of differential equation (d^(2)y)/(dx^(2))+(dy)/(dx)-6y=0

In each of the following find the coordinates of the point whose abscissa is the solution of the first equation and ordinate is the solution of the second equation: 5x(5-x)=1/2 (3-x), 4-3y= (4+y)/3

Show that y=a x^3+b x^2+c is a solution of the differential equation (d^3y)/(dx^3)=6a .

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

If t is real and lambda = (t^2-3t+4)/(t^2+3t+4) then find number of the solution of the systems of equation 3x-y+4z =0,x+2y-3z=-2.6x+5y+lambda z=-3 for a particular value of lambda .

Show that A=|[2,-3], [3 ,4]| satisfies the equation x^2-6x+17=0 . Hence, find A^(-1) .

- 3 x + 4y = 20 6 x + 3y = 15 If ( x, y ) is the solution to the system of equations above, what is the value of x ?