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일반적인 미적분학 문제
y^{''}-y^'+169y=13sin(13t)
y
′
′
−
y
′
+
1
6
9
y
=
1
3
sin
(
1
3
t
)
y^{''}+4y=sin(t),y(0)=0,y^'(0)=0
y
′
′
+
4
y
=
sin
(
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}-y=8xe^x+2e^x
y
′
′
−
y
=
8
xe
x
+
2
e
x
y^{''}+5y^'=4x+8
y
′
′
+
5
y
′
=
4
x
+
8
y^{''}-2y^'+y=(e^x)/(x^3)
y
′
′
−
2
y
′
+
y
=
e
x
x
3
y^{''}+4y=4csc^2(2t)
y
′
′
+
4
y
=
4
csc
2
(
2
t
)
(d^2y)/(dx^2)-5(dy)/(dx)+4y=e^x
d
2
y
dx
2
−
5
dy
dx
+
4
y
=
e
x
y^{'''}-y^{''}-25y^'+25y=7-e^x+e^{5x}
y
′
′
′
−
y
′
′
−
2
5
y
′
+
2
5
y
=
7
−
e
x
+
e
5
x
(D^2+D-2)y=e^x
(
D
2
+
D
−
2
)
y
=
e
x
y^{''}-8y^'+15y=e^{3x}sin(3x)
y
′
′
−
8
y
′
+
1
5
y
=
e
3
x
sin
(
3
x
)
x^{''}+a^2x=a^2b+c
x
′
′
+
a
2
x
=
a
2
b
+
c
y^{''}-10y^'+9y=5
y
′
′
−
1
0
y
′
+
9
y
=
5
y^{''}-8y^'+20y=200x^2-78xe^x
y
′
′
−
8
y
′
+
2
0
y
=
2
0
0
x
2
−
7
8
xe
x
y^{''}+y^'-12y=2cos(t)
y
′
′
+
y
′
−
1
2
y
=
2
cos
(
t
)
D^2(D-1)y=8e^{2x}
D
2
(
D
−
1
)
y
=
8
e
2
x
x^{''}-x^'-6x=2e^{4t}
x
′
′
−
x
′
−
6
x
=
2
e
4
t
y^{''}+ay=b
y
′
′
+
ay
=
b
y^{''}+3y^'+2y=e^{2x}
y
′
′
+
3
y
′
+
2
y
=
e
2
x
y^{''}+25y=3x,y(0)=1,y^'(0)=5
y
′
′
+
2
5
y
=
3
x
,
y
(
0
)
=
1
,
y
′
(
0
)
=
5
y^{'''}+7y^{''}+15y^'+9=1
y
′
′
′
+
7
y
′
′
+
1
5
y
′
+
9
=
1
y^{'''}-y^'=te^{-t}+2cos(t)
y
′
′
′
−
y
′
=
te
−
t
+
2
cos
(
t
)
x^{''}+9x=8sin(3t)
x
′
′
+
9
x
=
8
sin
(
3
t
)
(d^2y)/(dx^2)-4y=10e^{3x}
d
2
y
dx
2
−
4
y
=
1
0
e
3
x
x^{''}+2x^'+x=cos(2t)+3sin(2t)
x
′
′
+
2
x
′
+
x
=
cos
(
2
t
)
+
3
sin
(
2
t
)
(d^2y)/(dx^2)-(dy)/(dx)+y=x^3+6
d
2
y
dx
2
−
dy
dx
+
y
=
x
3
+
6
y^{''}+8y^'+17y=17x^2-x+28
y
′
′
+
8
y
′
+
1
7
y
=
1
7
x
2
−
x
+
2
8
(d^2y)/(dx^2)+4(dy)/(dx)+3y=e^{-2x}
d
2
y
dx
2
+
4
dy
dx
+
3
y
=
e
−
2
x
y^{''}-4y^'+5y=5t
y
′
′
−
4
y
′
+
5
y
=
5
t
(d^2y)/(dx^2)+y=x
d
2
y
dx
2
+
y
=
x
y^{''}-4y=4x^2e^{2x},y(0)=0,y^'(0)=0
y
′
′
−
4
y
=
4
x
2
e
2
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+9y= 1/((cos(3x))),y(0)=0,y^'(0)=0
y
′
′
+
9
y
=
1
(
cos
(
3
x
)
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}-25y=2
y
′
′
−
2
5
y
=
2
2y^{''}+y^'=2
2
y
′
′
+
y
′
=
2
y^{''}-2y^'-15y=4
y
′
′
−
2
y
′
−
1
5
y
=
4
y^{''}-3y^'-10y=54e^{7t}
y
′
′
−
3
y
′
−
1
0
y
=
5
4
e
7
t
(d^2y)/(dx^2)+5(dy)/(dx)+6y=cos(4x)
d
2
y
dx
2
+
5
dy
dx
+
6
y
=
cos
(
4
x
)
2y^{'''}-5y^'+3y=3x^2e^{2x}
2
y
′
′
′
−
5
y
′
+
3
y
=
3
x
2
e
2
x
y^{''}-6y^'+8y=-2e^{3x}
y
′
′
−
6
y
′
+
8
y
=
−
2
e
3
x
y^{''}+5y^'-5y=5t+9
y
′
′
+
5
y
′
−
5
y
=
5
t
+
9
y^{''}+y=3xcos(x)
y
′
′
+
y
=
3
x
cos
(
x
)
y^{'''}-2y^'-y^'+2y=(x+1)^2
y
′
′
′
−
2
y
′
−
y
′
+
2
y
=
(
x
+
1
)
2
y^{'''}-9y^{''}+27y^'-27y=e^{3x}
y
′
′
′
−
9
y
′
′
+
2
7
y
′
−
2
7
y
=
e
3
x
y^{''}-3y^'+2y= 1/(1+e^x)
y
′
′
−
3
y
′
+
2
y
=
1
1
+
e
x
2(d^2y)/(dx^2)-4(dy)/(dx)-6y=3e^{2x}
2
d
2
y
dx
2
−
4
dy
dx
−
6
y
=
3
e
2
x
y^{''}-4y^'=cosh(2x)
y
′
′
−
4
y
′
=
cosh
(
2
x
)
y^{''}+12y^'+27y=64e^{-1t},y(0)=5
y
′
′
+
1
2
y
′
+
2
7
y
=
6
4
e
−
1
t
,
y
(
0
)
=
5
y^{''}-y=e^tsin(t)
y
′
′
−
y
=
e
t
sin
(
t
)
y^{''}+3y^'-4y=3e^2x
y
′
′
+
3
y
′
−
4
y
=
3
e
2
x
y^{''}-2y^'-3y=e^x
y
′
′
−
2
y
′
−
3
y
=
e
x
y^{''}-2y^'+y=e^x(x^2-x+1)
y
′
′
−
2
y
′
+
y
=
e
x
(
x
2
−
x
+
1
)
y^{''}-2y^'+y=e^x 1/x
y
′
′
−
2
y
′
+
y
=
e
x
1
x
x^{''}+4x^'+40x=4e^{-2t}cos(6t)
x
′
′
+
4
x
′
+
4
0
x
=
4
e
−
2
t
cos
(
6
t
)
9y^{''}+30y^'+25y=2x+5
9
y
′
′
+
3
0
y
′
+
2
5
y
=
2
x
+
5
y^{''}+11y^'+5y=48e^{2x}
y
′
′
+
1
1
y
′
+
5
y
=
4
8
e
2
x
y^{''}+2y=e^x+2
y
′
′
+
2
y
=
e
x
+
2
y^{''}+y^'-2y=3e^{2x}
y
′
′
+
y
′
−
2
y
=
3
e
2
x
y^{'''}-5y^{''}+6y^'=6e^{2x}-2
y
′
′
′
−
5
y
′
′
+
6
y
′
=
6
e
2
x
−
2
y^{''}+2y^'+y=4e^{-x}
y
′
′
+
2
y
′
+
y
=
4
e
−
x
y^{''}+2y=8x+5
y
′
′
+
2
y
=
8
x
+
5
y^{''}+9y^'=cos(3t)
y
′
′
+
9
y
′
=
cos
(
3
t
)
(D^2+2D+1)y=xe^{-x}
(
D
2
+
2
D
+
1
)
y
=
xe
−
x
(d^2y)/(dx^2)-y=1
d
2
y
dx
2
−
y
=
1
y^{''}+y^'+1.25y=3cos(x)
y
′
′
+
y
′
+
1
.
2
5
y
=
3
cos
(
x
)
y^{''}=9+(y^')2
y
′
′
=
9
+
(
y
′
)
2
y^{''}+6y^'-27y=-105t+54t^2
y
′
′
+
6
y
′
−
2
7
y
=
−
1
0
5
t
+
5
4
t
2
y^{''}-6y^'+5y=x,y^1(0)=e^x
y
′
′
−
6
y
′
+
5
y
=
x
,
y
1
(
0
)
=
e
x
y^{''}-6y+9y=e^{3x}
y
′
′
−
6
y
+
9
y
=
e
3
x
y^{''}+4y=3csc^2(2x)
y
′
′
+
4
y
=
3
csc
2
(
2
x
)
3y^{''}-3y^'+y=-18+31x-11x^2+x^3
3
y
′
′
−
3
y
′
+
y
=
−
1
8
+
3
1
x
−
1
1
x
2
+
x
3
y^{''}+2/5 y^'+1/50 y=100
y
′
′
+
2
5
y
′
+
1
5
0
y
=
1
0
0
y^{''}-y^'-2y=e^{-t},y(0)=-1,y^'(0)=2
y
′
′
−
y
′
−
2
y
=
e
−
t
,
y
(
0
)
=
−
1
,
y
′
(
0
)
=
2
2y^{''}+9y^'-y=22
2
y
′
′
+
9
y
′
−
y
=
2
2
y^{''}-2y^'+y=(3+5x)e^{2x}
y
′
′
−
2
y
′
+
y
=
(
3
+
5
x
)
e
2
x
y^{'''}-2y^{''}+y^'=2,y^{''}(0)=-1
y
′
′
′
−
2
y
′
′
+
y
′
=
2
,
y
′
′
(
0
)
=
−
1
y^{''}-2y^'+2y=tcos(2t)
y
′
′
−
2
y
′
+
2
y
=
t
cos
(
2
t
)
y^{''}-2y^'+y=x^{(-1)/2}*e^x
y
′
′
−
2
y
′
+
y
=
x
−
1
2
·
e
x
y^{''}+2y^'+y=e^-xln(x)
y
′
′
+
2
y
′
+
y
=
e
−
x
ln
(
x
)
y^{''}+3y^'+2y=7x
y
′
′
+
3
y
′
+
2
y
=
7
x
y^{''}-y=x^2e^{-x}
y
′
′
−
y
=
x
2
e
−
x
y^{''}-2y^'-3y=8ex-9
y
′
′
−
2
y
′
−
3
y
=
8
ex
−
9
(D-1)(D-2)(D-3)y=e^x
(
D
−
1
)
(
D
−
2
)
(
D
−
3
)
y
=
e
x
y^{''}+5y^'+4y=24
y
′
′
+
5
y
′
+
4
y
=
2
4
d^2(d^2+4)y=96x^2
d
2
(
d
2
+
4
)
y
=
9
6
x
2
(d^2y)/(dt^2)+12(dy)/(dt)+32=32\H(t)
d
2
y
dt
2
+
1
2
dy
dt
+
3
2
=
3
2
H
(
t
)
y^{''''}+2y^{''}+y=9cos(2x)
y
′
′
′
′
+
2
y
′
′
+
y
=
9
cos
(
2
x
)
y^{''}+y=2sec(x)
y
′
′
+
y
=
2
sec
(
x
)
y^{''}+3y^'+2y=t^3e^{2t}
y
′
′
+
3
y
′
+
2
y
=
t
3
e
2
t
1/16 x^{''}+x=10sin(4t)
1
1
6
x
′
′
+
x
=
1
0
sin
(
4
t
)
y^{'''}-y^'=2x-3x^2
y
′
′
′
−
y
′
=
2
x
−
3
x
2
y^{'''}+y^{''}-5y^'+3y=2e^{(-3t)}+e^t
y
′
′
′
+
y
′
′
−
5
y
′
+
3
y
=
2
e
(
−
3
t
)
+
e
t
y^{''''}+2y^{''}+y=11+cos(2t)
y
′
′
′
′
+
2
y
′
′
+
y
=
1
1
+
cos
(
2
t
)
(d^2y)/(dx^2)-2(dy)/(dx)+y=3e^{2x}
d
2
y
dx
2
−
2
dy
dx
+
y
=
3
e
2
x
y^{''}-18y^'+81y=(x+1)e^x
y
′
′
−
1
8
y
′
+
8
1
y
=
(
x
+
1
)
e
x
4y^{''}+y=2sec(x/2)
4
y
′
′
+
y
=
2
sec
(
x
2
)
y^{''}+y^'-12y=2x
y
′
′
+
y
′
−
1
2
y
=
2
x
y^{''}+9y=9
y
′
′
+
9
y
=
9
y^{''}-5y^'-6y=3cos(x)+19sin(x)
y
′
′
−
5
y
′
−
6
y
=
3
cos
(
x
)
+
1
9
sin
(
x
)
y^{''}-4y=8x^2-2x
y
′
′
−
4
y
=
8
x
2
−
2
x
y^{''}+9y=1
y
′
′
+
9
y
=
1
u^{''}-a*\H(x)=x,u^'(-1)=0,u^'(1)=0
u
′
′
−
a
·
H
(
x
)
=
x
,
u
′
(
−
1
)
=
0
,
u
′
(
1
)
=
0
1
..
2350
2351
2352
2353
2354
..
2459