Solving of Nonhomogeneous Linear Differential Equations by Reduction of Order

بسم الله الرحمن الرحيم

Solving of Nonhomogeneous Linear Differential Equations by Reduction of Order


The nonhomogeneous diff. eq. with form second order ;
y +p(x)y +q(x)y=r(x) …..(1)
and y +p(x)y +q(x)y=0 …..(2)

Can be reduced to first order .To find the general solution for nonhomogeneous eq.(1) ;
Let y_1 (x) be a solution of the associated homogeneous equation(2) for eq.(1)
Let ?y(x)=v(x)y?_1 (x) be a solution of eq(1) ,and find the differentiation of y(x) ; y^ (x),y^ (x)
where v(x) is a twice-differentiable function to be determined




















The nonhomogeneous diff. eq. with form second order ;
y +p(x)y +q(x)y=r(x) …..(1)
and y +p(x)y +q(x)y=0 …..(2)

Can be reduced to first order .To find the general solution for nonhomogeneous eq.(1) ;
Let y_1 (x) be a solution of the associated homogeneous equation(2) for eq.(1)
Let ?y(x)=v(x)y?_1 (x) be a solution of eq(1) ,and find the differentiation of y(x) ; y^ (x),y^ (x)
where v(x) is a twice-differentiable function to be determined















The nonhomogeneous diff. eq. with form second order ;
y +p(x)y +q(x)y=r(x) …..(1)
and y +p(x)y +q(x)y=0 …..(2)

Can be reduced to first order .To find the general solution for nonhomogeneous eq.(1) ;
Let y_1 (x) be a solution of the associated homogeneous equation(2) for eq.(1)
Let ?y(x)=v(x)y?_1 (x) be a solution of eq(1) ,and find the differentiation of y(x) ; y^ (x),y^ (x)
where v(x) is a twice-differentiable function to be determined