谁能帮忙解下这个很难的微分方程,英文的,AsecondorderhomogeneousCauchy-EulerEquationisanequationofthetype:Question1:Assumingasolutionintheformy=x^mderivetheauxiliaryequationfortheC-EDEa

Question

谁能帮忙解下这个很难的微分方程,英文的,
     A second order homogeneous Cauchy-Euler Equation is an equation of the type:                 

Question 1:Assuming a solution in the form y=x^m derive the auxiliary equation for the C-E DE and give the general solution to the problem.                                                                                          

Question 2:Show that if the roots of theauxiliary equation are complex:m1,2=a+bi or a-bi,the general solution may be written as y(x)=x^a [c1*cos(b*ln(x)+c2*sin(b*lnx)).
 

Answer 1

个二阶齐次方程柯西欧拉方程的类型:问题1:假设一个解决方案在形式y = x ^ m获得辅助方程为汉英德,给一般的解决问题的办法.问题2:表明,如果theauxiliary方程的根是复杂的:m1,2 = + bi或bi,通常的解决方案可能会写成y(...