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\def\d{{\rm \,d}}
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{\Large MATH 411, Spring 2001} \\[2mm]
{\LARGE Homework 1} \\[2mm]
{\large Due: 30 January, 2001}\\[2mm]
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R. Redheffer, {\it Differential Equations}:

[2.1]: 3, 5, 12, 13(a);

[2.2]: 3(c,e,f), 5, 6, 9;

[2.3]: 2, 4, 6 (for 6 see the definition of first integral on page 38);

[2.4]: 4, 5, 6 (for 6 read about Bernoulli equation on page 43).

Check that following equations are in exact differntial form and solve them.
$$
\Bigl( 2x+\frac{x^2+y^2}{x^2 y} \Bigr)\d x=
\frac{x^2+y^2}{xy^2}\d y, \eqno{(a)}
$$
$$
\Bigl( \frac{\sin 2x}{y} + x \Bigr)\d x +
\Bigl( y - \frac{\sin^2 x}{y^2} \Bigr)\d y =0,\eqno{(b)}
$$
$$
\Bigl( \sin y + y\sin x + \frac{1}{x} \Bigr)\d x +
\Bigl( x\cos y - \cos x + \frac{1}{y} \Bigr)\d y = 0,\eqno{(c)}
$$
$$
\frac{2x\d x}{y^3}+\frac{(y^2-3x^2)\d y}{y^4}=0,\qquad y\Big|_{x=1} = 1.\eqno{(d)}
$$


All problems are estimated by 5 points, except 12 in [2.1], 3 in [2.2], 6 in [2.3], 6 in [2.4], d, 
which are estimated by 7 points. 
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