Match each differential equation to a function which is a solution. FUNCTIONS A. y=3x+x^2, B. y=e^(-5x), C. y=sin(x), D. y=x^(1/2), E. y=5exp(2x),
DIFFERENTIAL EQUATIONS

Match the following differential equations with their solutions. The symbols A, B, C in the solutions stand for arbitrary constants. You must get all of the answers correct to receive credit.

For what values of r does the function y=2e^(rx) satisfy the differential equation y''-13y'+36y=0?
The smaller one is .
The larger one (possibly the same) is .

The solution of a certain differential equation is of the form

y(t)=aexp(7t)+bexp(12t)

where a and b are constants.
The solution has initial conditions y(0)=3 and y'(0)=4 Find the solution by using the initial
conditions to get linear equations for a and b.