解dy/dx=y/x+tany/x 的微分方程

令 y/x = t => y = x * t => dy = x dt + t dx => dy/dx = t + x dt/dx 代入原方程得：t + x dt/dx = t + tan t => x * dt/dx = tan t => cot t dt = 1/x dx 积分=> ln |sin t| = ln x + C => sin t = C1 * e^x => (...