# Ecuacion diferencial

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• Publicado : 30 de mayo de 2011

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NOMBRE: DONNY NAYMAR ESCALANTE OJEDA
CODIGO:2009218164
6.- y'''-2y''-y'+2y=0
>> dsolve('D3y-2*D2y-Dy+2*y=0','x')
ans =
C1*exp(2*x)+C2*exp(x)+C3*exp(-x)
7. - y'''+3y''-3y'+y=0
>>dsolve('D3y+3*D2y-3*Dy+y=0','x')
ans =C1*exp(-x*2^(2/3)-x*2^(1/3)-x)+C2*exp(1/2*x*2^(2/3)+1/2*x*2^(1/3)-x)*sin(1/2*3^(1/2)*2^(2/3)*x-1/2*3^(1/2)*2^(1/3)*x)+C3*exp(1/2*x*2^(2/3)+1/2*x*2^(1/3)-x)*cos(1/2*3^(1/2)*2^(2/3)*x-1/2*3^(1/2)*2^(1/3)*x)
8. - y'''-y''+y'+y=0
>> dsolve('D3y-D2y-Dy+y=0','x')
ans =
C1*exp(-x)+C2*exp(x)+C3*exp(x)*x
9. - y'''-y=0
>> dsolve('D3y-y=0','x')
ans =
C1*exp(x)+C2*exp(-1/2*x)*sin(1/2*3^(1/2)*x)+C3*exp(-1/2*x)*cos(1/2*3^(1/2)*x)
10. - yIV-y=0
>> dsolve('D4y-y=0','x')
ans =
C1*exp(x)+C2*exp(-x)+C3*sin(x)+C4*cos(x)
11.-y'''-y'-2y''=0 ; y(0)=1, Y’(0)=1
>> dsolve('D3y-Dy-2*Dy=0','y(0)=1' ,' Dy(0)=1','x')
ans =
1-2*C2+1/3*3^(1/2)+C2*exp(3^(1/2)*x)+(-1/3*3^(1/2)+C2)*exp(-3^(1/2)*x)

12.- y''-6y'+9y=0 ; y(0)=1, Y’(0)=2
>> dsolve('D2y-6*Dy+9*y=0','y(0)=1' ,' Dy(0)=2')
ans =
exp(3*t)-exp(3*t)*t
13.- y''-8y'-9y=0 ; y(1)=1, Y’(0)=0
>> dsolve('D2y-8*Dy-9*y=0','y(1)=1' ,' Dy(0)=0')ans =
9/(9*exp(-1)+exp(9))*exp(-t)+1/(9*exp(-1)+exp(9))*exp(9*t)
14.- y''-4y=0 ; y(0)=1, Y’(0)=1
>> dsolve('D2y-4*y=0','y(0)=1' ,' Dy(0)=1')
ans =
3/4*exp(2*t)+1/4*exp(-2*t)
15.- y''-4y'+5y=0 ; y(0)=1, Y’(0)=0
>> dsolve('D2y-4*Dy-5*y=0','y(0)=1' ,' Dy(0)=0')
ans =
5/6*exp(-t)+1/6*exp(5*t)
16.- y'''+y'=0 ; y ’’(0)=1, Y ’’(0)=1 , y (0)=0
>>dsolve('D3y+Dy=0','D2y(0)=1',' y(0)=0')
ans =
1+C2*sin(t)-cos(t)
17.- y'''=y' ; y (0)=2 , Y ’(0)=0 , y ‘’ (0)=-1
>> dsolve('D3y=Dy','D2y(0)=-1',' Dy(0)=0','y(0)=2')
ans =
3-1/2*exp(t)-1/2*exp(-t)

18.- y'''-y''-4y'+4y=0 ; cuando X=0 ; Y(0)=0 , y ’(0) = -1 ; y ’’ (0)= 5
>> dsolve('D3y-D2y-4*Dy+4*y=0','y(0)=0' ,'y(0)=0' ,' Dy(0)=-1','D2y(0)=5')
ans =
-5/3*exp(t)+exp(2*t)+2/3*exp(-2*t)19.- y''-y=0 ; cuando X=0 ; Y=Y0 , y ’= 0
>> dsolve('D2y-y=0',' y(0)=0','Dy(0)=0')
ans =
0
20.- yIV+3y '''+2y''=0 ; cuando X=0 ; Y=0 , y ’= 4 , y ’’ = -6
>> dsolve('D4y+3*D3y+2*D2y=0','y(0)=0' ,'Dy(0)=4' ,'D2y(0)=-6')
ans =
6+3*C3+(-2-2*C3)*t+C3*exp(-2*t)+(-6-4*C3)*exp(-t)
21. >> dsolve('D2y+y=0','y(0)=0','Dy(0)=0','x')

ans =

0

22. >>dsolve('D4y+3*D3y+2*D2y=0','y(0)=0','Dy(0)=4','D2y(0)=-6','x')

ans =

6+3*C4+(-2-2*C4)*x+(-6-4*C4)*exp(-x)+C4*exp(-2*x)

23. >> dsolve('D2y-Dy=x^2','x')
ans =

-x^2-1/3*x^3+C1*exp(x)-2*x+C2

24. >> dsolve('D2y-4*Dy-5*y=5*x','x')

ans =

C2*exp(-x)+exp(5*x)*C1+4/5-x

25. >> dsolve('D3y-Dy=x+1','x')

ans =

C2*exp(x)-C1*exp(-x)-1/2*x^2-x+C326. >> dsolve('D2y-4*Dy+4*y=4*(x-1)','x')

ans =

exp(2*x)*C2+exp(2*x)*x*C1+x

27. >> dsolve('D2y+2*Dy+2*y=2*((x-1)^2)','x')

ans =

exp(-x)*sin(x)*C2+exp(-x)*cos(x)*C1+x^2-4*x+4

28. >> dsolve('D3y+D2y+Dy+y=x^2+2*x-2','x')

ans =

-4+x^2+cos(x)*C1+sin(x)*C2+C3*exp(-x)

29. >> dsolve('D4y+4*D2y=8*(6*x^2+5)','x')

ans =-1/4*sin(2*x)*C2-1/4*cos(2*x)*C1+x^4+2*x^2+C3*x+C4

30. >> dsolve('D3y-3*D2y+3*Dy-y=(2-x)^2','x')

ans =

-4-2*x-x^2+C1*exp(x)+C2*exp(x)*x+C3*exp(x)*x^2

31. >> dsolve('2*D2y-9*Dy+4*y=18*x-4*x^2','x')

ans =

exp(4*x)*C2+exp(1/2*x)*C1+1-x^2

32. >> dsolve('D4y-2*D2y+y=x^2-5','x')

ans =

-1+x^2+C1*exp(x)+C2*exp(-x)+C3*exp(x)*x+C4*exp(-x)*x

33. >>dsolve('D2y+Dy-2*y=2*x','y(0)=0','Dy(0)=1','x')

ans =

exp(x)-1/2*exp(-2*x)-1/2-x

34. >> dsolve('D3y+4*Dy=x','y(0)=0','Dy(0)=0','D2y(0)=1','x')

ans =

-3/16*cos(2*x)+3/16+1/8*x^2

35. >> dsolve('D3y+4*Dy=x','y(0)=0','Dy(0)=0','D2y(0)=1','x')

ans =

-3/16*cos(2*x)+3/16+1/8*x^2

36. >> dsolve('D2y-6*y+9*y=x^2-x+3','y(0)=3/4','Dy(0)=1/27','x')...