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in this video were going to talk about how to solve the initial value problem as it relates to differential equations so lets start with this example problem first let me adjust the size on this so lets say that d y over dx is equal to six x minus three and were given the point y of zero is equal to four so this means that x is 0 and y is 4. how can we solve this differential equation the first thing im going to do is multiply both sides by dx so i have d y is equal to 6x minus 3 times dx so i like to separate the variables i like to separate y from x once the variables are separated we can integrate both sides so the integral of d y is simply y the antiderivative of x or x to the first power is x squared over 2 times the constant that was in front of it which is six the antiderivative of a constant is just that constant times x and of course we need our constant of integration c so this right here is the general solution to the differential equation but now we need to plug in our
