>>814

定数変化法により

(1) 与式に 1/x^2 を掛けて
　(d/dx)(y/x^2) = (2/x) - (3/x^2),
　y/x^2 = 2･log|x| + 3/x + c1,
　y = 2x^2･log|x| +3x + c1･x^2,

(2) 与式にxを掛けて
　(dy/dx)(xy) = 3x^2 + 2x,
　xy = x^3 + x^2 + c2,
　y = x^2 + x + c2/x,

(3) 与式にxを掛けて
　(dy/dx)(xy) = 1/x,
　xy = log|x| + c3,
　y = (1/x)log|x| + c3/x,

(4) 与式に x^2 を掛けて
　(d/dx)(x^2･y) = x^3 - 2x^2,
　x^2･y = (1/4)x^4 - (2/3)x^3 + c4,
　y = (1/4)x^2 - (2/3)x + c4/x^2,