(4x-1)y''-4y'=0[y'/(4x-1)]'=0 (4x-1≠0)y'=C1(4x-1)y=C1(2x^2-x)+C2当4x-1=0时,原方程化为y'=0,即y=C所以方程通解为y=C1(2x^2-x)+C2
方法如下图所示,请认真查看,祝学习愉快: