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from Ekeeda Hello friends in this video we are going to see problems based on
solution of differential equation so let us start with problem number show that Y
square is equal to ax square is a solution of the differential equation x
dy by DX square minus 2y Dy by DX plus ax is equal to 0 the subs that we have
seen in the previous videos which were based on formation of differential
equation and this sums are similarly but only the difference is that in that sums
the equation was given and the question was to find a differential equation but
here the equations also give a differential equation is also given only
you need to prove that the differential equation of this is the result given so
let us see how to obtain the differential equation of Y square is
equal to ax square we have only one arbitrary constant therefore first we
differentiate it this will give you Y into dy by DX is
equal to a2 2x who will be cancelled and why do you have a DX will be equal to ax so dy by DX will be ax upon Y as you can
see in its differential equation you cannot see a higher order derivative so
no need to differentiate it further we have dy by DX now let us consider the
LHS of this part and start solving it it should be 0 now let us consider the LHS
of this equation and substitute dy by DX as ax upon y on solving it if we get 0
it makes the differential equation of this equation is type so in the left hand side of the
differential equation we have X in two divided by DX the whole square minus 2y
dy by DX plus ax now let us substitute the value of dy by DX that we have
obtained it was ax of so after substitution we have X into a X
by Y the whole square minus 2y again we have dy by DX as a X upon y plus ax this
will give you X this will give you X into a square X
square upon y squared minus 2x plus ax now the value of y Square it is already
given as X square so this will give you X into a square X
square upon DX square minus 2x plus ax your money will be cancelled and X
square will be cancelled the remaining part will be a X minus 2ax plus ax now ax plus ax
will give you 2 X followed by -2 X that will be equal to 0 and that is our edges
finally we can see the equation y square is equal to aah square is the solution of the given
differential equation I hope friends here understood this
problem thank you for watching this video stay tuned with the heater and
subscribe Twiggy de you

Solution Of Differential Equation Problem No 1 – Differential Equations – Diploma Maths II