求下列方程的特解y*(1)2y''+y'-y=2e^x(2)y''-3y=x^2+1(3)y''-6y'+9y=5(x+1)e^3x(4)y''-3y'+2y=x^2*e^x(5)y''-2y'+10y=e^x*sin2x(6)y'-2y'+10y=e^x*con2x(7)y''+4y=xconx前面三题只需要答案就好,后面的四题最好有过程,回答的全面

Question

求下列方程的特解y*
(1) 2y''+y'-y=2e^x
(2)y''-3y=x^2+1
(3)y''-6y'+9y=5(x+1)e^3x
(4)y''-3y'+2y=x^2*e^x
(5)y''-2y'+10y=e^x*sin2x
(6)y'-2y'+10y=e^x*con2x
(7)y''+4y=xconx
前面三题只需要答案就好,后面的四题最好有过程,回答的全面有加分奥!
要考试的呀，所以想要确认一下为！呵呵，拜托大家老！

Answer 1

都是通解喔
1 y(x) = exp(-x)*C2+exp((1/2)*x)*C1+exp(x)
2 y(x) = exp(sqrt(3)*x)*C2+exp(-sqrt(3)*x)*C1-5/9-(1/3)*x^2
3 y(x) = exp(3*x)*C2+exp(3*x)*x*C1+(5/27)*e^3*(4+7*x+3*x^2)
4 y(x) = (-2*x-x^2-(1/3)*x^3+exp(x)*C1+C2)*exp(x)
5 y(x) = exp(x)*sin(3*x)*C2+exp(x)*cos(3*x)*C1+(1/5)*exp(x)*sin(2*x)
con 就是cos吧
6是y''-2y'+10y=e^x*cos2x 吧
6 y(x) = exp(x)*sin(3*x)*C2+exp(x)*cos(3*x)*C1+(1/5)*exp(x)*cos(2*x)
7 y(x) = sin(2*x)*C2+cos(2*x)*C1+(2/9)*sin(x)+(1/3)*x*cos(x)
都是用的软件