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silent_storm · Nov 1, 2010, 09:29 AM

a) Solve the given differential equation by Separation of variables.

sec2xdy+cscydx=0

b)Solve the following Differential Equation

ï»¿(y2+3xy)dx=(4x2+xt)dy, y(1)=1

c)Determine whether the following Differential Equation is exact. If exact, solve

(1-2x2-2y)dy/dx=4x3+4xy

ITS URGENT NEED WITHIN 24 hours

galactus · Nov 1, 2010, 01:10 PM

#1:

$sec(2x)dy+csc(y)dx=0$

$sec(2x)dy=-csc(y)dx$

Separate variables:

$\frac{dy}{-csc(y)}=\frac{dx}{sec(2x)}$

Now, integrate:

For the other two, I can not read them for certain. Try using ^ (SHIFT 6) if you mean an exponent.

I am going to hazard a guess and presume that #2 is:

$(y^{2}+3xy)dx=(4x^{2}+xy)dy$ ?

#3: $(1-2x^{2}-2y)dy-(4x^{3}+4xy)dx=0$ ?

$M(x,y)=4x^{3}+4xy, \;\ N(x,y)=1-2x^{2}-2y$

Check if $\frac{{\partial}M}{{\partial}y}=\frac{{\partial}N} {{\partial}x}$

If this is true, then it is exact.