Answer laterWhich is the most recommended mathematics guide to refer to the Differential Equations concept?
dy/dx=sin ( x + y) + cos ( x + y )
Hello Aspirant,
Hope you are doing well!!
It is quite difficult to make integration sign, In place of integration sign I'll put |, and in place of power I'll put ** when you are solve in your notebook you can place | sign to integration sign and ** to power sign.
Let X+Y = v
1 + dY/dX = dv/dX
dY/dX= dv/dX-1
dY/dX = sin (X + Y) + cos (X + Y)
dv/dX - 1 = sin v + cos v
dv / (1+cos v + sin v) = dX
Integrate both side
| dv / (1 + cos v + sin v ) = | dX | dv / ( 1 + ((1 - tan**2 (v/2)) / (1 + tan** 2 (v/2)) + ((2 tan (v/2) / (1 + tan **2 (v/2))
= |dX | sec**2 (v/2) dv / (2(1+ tan(v/2))
=|dx log (1 + tan (v/2)
= X+ c log ( 1+ tan (X + Y) / 2) = X + c
I hope this will help you.
Feel free to ask any query.
solve the given question (xlogx)dy/dx+y=logx^2
Hello,
This question is very simple. Divide the equation by x. logx, on both sides.
So we get :
dy/dx + y/ x.logx = 2. logx / x .logx
i.e. dy/dx + y/ x logx = 2/x
Clearly this is a linear differential equation. So firstly we find the integrating factor.
I.F. = e ^ ( intg. { 1/ xlogx dx } ) ,
I.F. = logx
Now the solution of this differential equation is given by
y. I.F = intg. ( Q. I.F dx ) where Q = 2/x
Hence solution is : y. logx = (logx)^2 + c
Hope it helps.
