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linear equations - resolving and identifying linear first order differential equationsseparable equations - resolving and identifying separable first
in this section we will consider for solving first order differential equations the most common first order differential equation can be written
it may seem like an odd question to ask and until now the answer is not all the time yes just as we identify that a solution to a differential
all differential equations will doesnt have solutions thus its useful to identify ahead of time if there is a solution or not why waste our time
if a differential equation does have a solution how many solutions are thereas we will see ultimately this is possible for a differential equation to
reflexive relationsr is a reflexive relation if a a euro r a euro a it could be noticed if there is at least one member a euro a like a a euro
find the length of the second diagonal of a rhombus whose side is 5cm and one of the diagonals is
relations in a setlet consider r be a relation from a to b if b a then r is known as a relation in a thus relation in a set a is a subset of a
newtons second law of motion which recall from the earlier section that can be written asmdvdt f tvhere ftv is the sum of forces which act on the
find the ratio in which the line segment joining a65 and b4-3 is divided by the line y2 ans35ans let the
this topic is specified its own section for a couple of purposes firstly understanding direction fields and what they tell us regarding a
plot the points a20 and b 60 on a graph paper complete an equilateral triangle abc such that the ordinate of c be a positive real number find the
determine an actual explicit solution to yprime ty y2 -1solution we already identify by the previous illustration that an implicit solution to this
the vertices of a abc are a4 6 b1 5 and c7 2 a line is drawn to intersect sides ab and ac at d and e respectively such that adab aeac 14 calculate
y2 t2 - 3 is the actual implicit solution to y ty y2 -1 at such point i will ask that you trust me that it is actually a solution to the
its easier to describe an explicit solution in this case and then tell you what an implicit solution is not and after that provide you an
the actual solution is the specific solution to a differential equation which not only satisfies the differential equation although also satisfies
the general solution to a differential equation is the most common form which the solution can take and does not take any initial conditions in
the interval of validity for an ivp along with initial conditionsyt0 y0 orand ykt0 ykthere is the largest possible interval on that the solution is
suppose a and b be two non-empty sets then every subset of a chi b describes a relation from a to b and each relation from a to b is subset of
an ivp or initial value problem is a differential equation with an appropriate number of initial conditionsillustration 3 the subsequent is an ivp4x2
find the relation between x and y when the point xy lies on the straight line joining the points 2-3 and 14 hint use area of triangle is 0ans
initial conditions are a set of conditions or a condition on the solution which will permit us to find out that solution which we are after
the midpoint of the line joining 2a 4 and -2 3b is 1 2a 1find the values of a amp b ans a 2 b 2ans a2a
find the coordinates of the point p which is three -fourth of the way from a 3 1 to b -2