A homogeneous second-order linear differential equation, two functions y1 and y2 , and a pair of initial conditions are given below. First verify that y1 and y2 are solutions of the differential equation. Then find a particular solution of the form y = c1y1 + c2y2 that satisfies the given initial conditions.
y'' + 49y = 0; y1 = cos(7x) y2 = sin(7x); y(0) = 10 y(0)=-4
y(x)=?

Step-by-step explanation:

Check part

Now, replace to the original one.

Done!!

Particular solution

I believe that y'(0) = 4, not y(0) anymore. Since y(0) CANNOT have two different solution.

The last step is to put C1, C2 into your solution. You finish it.

you never say the total so we cant find the percentage used for petrol

step-by-step explanation:

6 and 24

step-by-step explanation:

6 x 4 = 24