演習問題1.5

1.: 次の微分方程式の一般解を求めよ．
(a): $\displaystyle{(x - y^{2})dx + 2xydy = 0}$
(b): $\displaystyle{(5xy + 4y^{2} + 1)dx + (x^{2} + 2xy)dy = 0}$
(c): $\displaystyle{(2xy^{2} + y)dx + (2y^{3} - x)dy = 0}$
(d): $\displaystyle{(2x + \tan{y})dx + (x - x^{2}\tan{y})dy = 0}$
2.: 次の微分方程式を解け．
(a): $\displaystyle{(2y^{2} - xy)dx + (2x^{2} - 3xy)dy = 0}$
(b): $\displaystyle{(y^{4} + 2x^{3}y)dx - (x^{4} + 2xy^{3})dy = 0}$