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Solve :
x²y" -2xy' -4y=x²+2ln x
Solve :
dy/dx= 1/x+y+1
Solve :
P² -2xyp + 4y²=0, where p=dy/dx
Using the method of variation of parameters, solve the equation:
d²y/dx² +a²y = sec ax.
Solve:
x²y²(2ydx + xdy) - (5ydx + 7xdy) =0
Examine whether the second order partial derivatives of f at (0,0) exist or not if
f :R² ➡R is defined by
f(x, y) ={x²y/√x+y² , xy≠0 and 0, xy=0
Let f(x, y) ={ y³ /x² + y² if (x, y) ≠(0, 0) and 0 otherwise
Show that f is continuous but not differentiable at (0, 0).
Check whether the limit of the function
f(x, y) = 4x²y/ x^10 +3y² exist as (x, y) ➡(0, 0)
Show that the closed sphere with centre (1,3,5) and radius 8 in R³ is contained in the
open cube
P ={(x, y, z): | x -1| <10, | y - 3 | < 10, | z - 5 | <10}.
Find the cylindrical coordinates of the points where the Cartesian coordinates are :
(√5, 1,2)
