方程d^4y/dx^4-(1/x)*(d^3y/dx^3)=0的通解

Question

方程d^4y/dx^4-(1/x)*(d^3y/dx^3)=0的通解

Answer 1

xy^(4)-y^(3)=0
(xy^(4)-y^(3))/x^2=0
(y^(3)/x)'=0
两边积分：y^(3)/x=C1
y^(3)=C1x
两边积分：y''=C1x^2+C2
两边积分：y'=C1x^3+C2x+C3
两边积分：y=C1x^4+C2x^2+C3x+C4