Solution of Differential Equations by Power Series

بسم الله الرحمن الرحيم

Solution of Differential Equations by Power Series :


We can solve the linear differential equations with variable coefficients , through ;
suppose the solution as power series for x (that series must be convergent ,differentiable ),
y=c_0+c_1 x+c_2 x^2+?+c_n x^n+?
To find the coefficients c_0,c_1 ,c_2 ,…,c_n .find
y^ =c_1+2c_2 x+?3c?_3 x^2+?+nc_n x^(n-1)+?
and then substitute it on y ,y , y ,… ,in original equation
find power coefficients of x from similar sides .







































We can solve the linear differential equations with variable coefficients , through ;
suppose the solution as power series for x (that series must be convergent ,differentiable ),
y=c_0+c_1 x+c_2 x^2+?+c_n x^n+?
To find the coefficients c_0,c_1 ,c_2 ,…,c_n .find
y^ =c_1+2c_2 x+?3c?_3 x^2+?+nc_n x^(n-1)+?
and then substitute it on y ,y , y ,… ,in original equation
find power coefficients of x from similar sides .
































We can solve the linear differential equations with variable coefficients , through ;
suppose the solution as power series for x (that series must be convergent ,differentiable ),
y=c_0+c_1 x+c_2 x^2+?+c_n x^n+?
To find the coefficients c_0,c_1 ,c_2 ,…,c_n .find
y^ =c_1+2c_2 x+?3c?_3 x^2+?+nc_n x^(n-1)+?
and then substitute it on y ,y , y ,… ,in original equation
find power coefficients of x from similar sides .