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일반적인 미적분학 문제
y^{''}-6y^'+9y=e^{3x}(x^2-4x+5)
y
′
′
−
6
y
′
+
9
y
=
e
3
x
(
x
2
−
4
x
+
5
)
y^{''}+2y=e^t+2
y
′
′
+
2
y
=
e
t
+
2
y^{''}-5y^'+9y=xe^x
y
′
′
−
5
y
′
+
9
y
=
xe
x
y^{''}-y^'-30y=2x+4
y
′
′
−
y
′
−
3
0
y
=
2
x
+
4
x^{''}+4x=1
x
′
′
+
4
x
=
1
y^{''}+y=5xsin(5x)
y
′
′
+
y
=
5
x
sin
(
5
x
)
(D^4+2D^3+2D^2)y=2xe^{-x}
(
D
4
+
2
D
3
+
2
D
2
)
y
=
2
xe
−
x
(d^2y)/(dx^2)+4(dy)/(dx)-12=0
d
2
y
dx
2
+
4
dy
dx
−
1
2
=
0
y^{''}+4y^'+5y=(2e^{2x})/(sin(x))
y
′
′
+
4
y
′
+
5
y
=
2
e
2
x
sin
(
x
)
y^{''}+9y=t^2e^{3t}
y
′
′
+
9
y
=
t
2
e
3
t
y^{''}+16y=8cos(4x)+12sin(4x)
y
′
′
+
1
6
y
=
8
cos
(
4
x
)
+
1
2
sin
(
4
x
)
(d^2x)/(dt^2)+9x=5sin(3t)
d
2
x
dt
2
+
9
x
=
5
sin
(
3
t
)
y^{''}-y^'-2y=(6x^2+8x+7)e^x
y
′
′
−
y
′
−
2
y
=
(
6
x
2
+
8
x
+
7
)
e
x
y^{''}-2y^'-3y=(3x^2-5)e^{-x}
y
′
′
−
2
y
′
−
3
y
=
(
3
x
2
−
5
)
e
−
x
2y^{''}-8y=16e^x
2
y
′
′
−
8
y
=
1
6
e
x
(d^3-3d-2)y=540x^3e^{-x}
(
d
3
−
3
d
−
2
)
y
=
5
4
0
x
3
e
−
x
y^{''}+y=2sin(2t),y(0)=9,y^'(0)=0
y
′
′
+
y
=
2
sin
(
2
t
)
,
y
(
0
)
=
9
,
y
′
(
0
)
=
0
y^{''}+4y=sec(x)
y
′
′
+
4
y
=
sec
(
x
)
y^{''}+2y^'+y=((e^x))/x
y
′
′
+
2
y
′
+
y
=
(
e
x
)
x
y^{''}+2y^'+y=cos(5t)
y
′
′
+
2
y
′
+
y
=
cos
(
5
t
)
y^{''}+5y^'=2x^3-4x^2-x+6
y
′
′
+
5
y
′
=
2
x
3
−
4
x
2
−
x
+
6
y^{''}+8y^'+16y=3(e^{-4x})/(x^4)
y
′
′
+
8
y
′
+
1
6
y
=
3
e
−
4
x
x
4
y^{''}+2*y^'+y=e^{-t}
y
′
′
+
2
·
y
′
+
y
=
e
−
t
y^{''}-y=6e^{2x},y(0)=4,y^'(0)=4
y
′
′
−
y
=
6
e
2
x
,
y
(
0
)
=
4
,
y
′
(
0
)
=
4
선의 y^{''}+2y^'+2y=e^{-x}cos(x)
linear
y
′
′
+
2
y
′
+
2
y
=
e
−
x
cos
(
x
)
y^{''}-6y^'+9y=e^{2t}
y
′
′
−
6
y
′
+
9
y
=
e
2
t
(D^4-1)*y=sin(2x)
(
D
4
−
1
)
·
y
=
sin
(
2
x
)
y^{''}+y^'-7y=42t
y
′
′
+
y
′
−
7
y
=
4
2
t
y^{''}+y=2,y(0)=2,y(0)=0
y
′
′
+
y
=
2
,
y
(
0
)
=
2
,
y
(
0
)
=
0
y^{''}-6y^'-9y=x^2+e^x
y
′
′
−
6
y
′
−
9
y
=
x
2
+
e
x
x^{''}+5x^'+4x=t^2+3t+5
x
′
′
+
5
x
′
+
4
x
=
t
2
+
3
t
+
5
y^{''}-2y^'+y=2sin(3x)
y
′
′
−
2
y
′
+
y
=
2
sin
(
3
x
)
y^{''}+16y=e^{3t}
y
′
′
+
1
6
y
=
e
3
t
y^{''}+16y=2cos(4x)
y
′
′
+
1
6
y
=
2
cos
(
4
x
)
y^{''}-10y^'+25y=48e^x
y
′
′
−
1
0
y
′
+
2
5
y
=
4
8
e
x
y^{''}-y^'-2y=1-x,y(0)=0,y^'(0)=0
y
′
′
−
y
′
−
2
y
=
1
−
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}-2y^{''}+y=4e^x+4e^{-x}
y
′
′
−
2
y
′
′
+
y
=
4
e
x
+
4
e
−
x
2y^{''}+4y=6t,y(0)=0,y^'(0)=0
2
y
′
′
+
4
y
=
6
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+4y=t^2+6e^t,y(0)=0,y^'(0)=0
y
′
′
+
4
y
=
t
2
+
6
e
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+4y=t^2+6e^t,y(0)=0,y^'(0)=9
y
′
′
+
4
y
=
t
2
+
6
e
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
9
x^{''}+x=9cos(4t)
x
′
′
+
x
=
9
cos
(
4
t
)
y^{''}-4y=3e^{2t}
y
′
′
−
4
y
=
3
e
2
t
9y^{''}+7y^'-y=24
9
y
′
′
+
7
y
′
−
y
=
2
4
y^{''}+16y=8x+8sin(x)
y
′
′
+
1
6
y
=
8
x
+
8
sin
(
x
)
y^{'''}+6y^{''}+12y^'+8y=4e^{-2x}
y
′
′
′
+
6
y
′
′
+
1
2
y
′
+
8
y
=
4
e
−
2
x
y^{''}-3y^'=x^2-1
y
′
′
−
3
y
′
=
x
2
−
1
9y^{''}+24y^'+16y=8e^x
9
y
′
′
+
2
4
y
′
+
1
6
y
=
8
e
x
y^{''}-4y^'+4y=25cos(x)
y
′
′
−
4
y
′
+
4
y
=
2
5
cos
(
x
)
x^{''}-x=e^{-t}sin(e^{-t})+cos(e^{-t})
x
′
′
−
x
=
e
−
t
sin
(
e
−
t
)
+
cos
(
e
−
t
)
y^{''}-2y^'-3y=2ex-10
y
′
′
−
2
y
′
−
3
y
=
2
ex
−
1
0
y^{'''}+3y^{''}+y^'-5y=-5x
y
′
′
′
+
3
y
′
′
+
y
′
−
5
y
=
−
5
x
y^{''}+4y=4sin(2t)+8cos(2t)
y
′
′
+
4
y
=
4
sin
(
2
t
)
+
8
cos
(
2
t
)
y^{''}+4y=2cos(x)
y
′
′
+
4
y
=
2
cos
(
x
)
y^{''}+7y=5t^2-5,y(0)=0,y^'(0)=-2
y
′
′
+
7
y
=
5
t
2
−
5
,
y
(
0
)
=
0
,
y
′
(
0
)
=
−
2
y^{'''}+y^'=sec^2(x)
y
′
′
′
+
y
′
=
sec
2
(
x
)
y^{'''}-5y^{''}+6y^'=9+2sin(x)
y
′
′
′
−
5
y
′
′
+
6
y
′
=
9
+
2
sin
(
x
)
y^{''}-y=e^xsin(x)
y
′
′
−
y
=
e
x
sin
(
x
)
4y^{''}-4y^'+y=16e^{(x/2)}
4
y
′
′
−
4
y
′
+
y
=
1
6
e
(
x
2
)
(d^2y)/(dx^2)+2(dy)/(dx)-y=20xe^x
d
2
y
dx
2
+
2
dy
dx
−
y
=
2
0
xe
x
x^{''}+3x^'-10x=6e^{4t}
x
′
′
+
3
x
′
−
1
0
x
=
6
e
4
t
(d^2y)/(dx^2)+(dy)/(dx)+7y=e^{5x}
d
2
y
dx
2
+
dy
dx
+
7
y
=
e
5
x
y^{''}-4y^'+3y=2x
y
′
′
−
4
y
′
+
3
y
=
2
x
y^{''}+y= 1/((sin(x))^3)
y
′
′
+
y
=
1
(
sin
(
x
)
)
3
(D^2-4D+4)y=8e^{2x}x^2sin(2x)
(
D
2
−
4
D
+
4
)
y
=
8
e
2
x
x
2
sin
(
2
x
)
x^{''}-x=-1
x
′
′
−
x
=
−
1
y^{''}+6y^'+9y=cos(3x)
y
′
′
+
6
y
′
+
9
y
=
cos
(
3
x
)
3y^{''}-10y^'-13y=13x-3
3
y
′
′
−
1
0
y
′
−
1
3
y
=
1
3
x
−
3
y^{''}+2y^'-3y=te^{-3t}
y
′
′
+
2
y
′
−
3
y
=
te
−
3
t
y^{'''}+25y^'=10sin(5x)-4x^2
y
′
′
′
+
2
5
y
′
=
1
0
sin
(
5
x
)
−
4
x
2
y^{''}+4y^'+8y=e^{2x}(sin(2x)+cos(2x))
y
′
′
+
4
y
′
+
8
y
=
e
2
x
(
sin
(
2
x
)
+
cos
(
2
x
)
)
y^{''}+2y^'+y=x+e^x
y
′
′
+
2
y
′
+
y
=
x
+
e
x
y^{''}+y=e^{t^2}
y
′
′
+
y
=
e
t
2
y^{''}-3y+2y=e^tsin(t)
y
′
′
−
3
y
+
2
y
=
e
t
sin
(
t
)
y^{''}-2y^'+y=x^2-x-3
y
′
′
−
2
y
′
+
y
=
x
2
−
x
−
3
y^{''}+2y^'+y=2xsin(x)
y
′
′
+
2
y
′
+
y
=
2
x
sin
(
x
)
y^{''}+3y^'+2y=x^3+4x^2+2x+1
y
′
′
+
3
y
′
+
2
y
=
x
3
+
4
x
2
+
2
x
+
1
y^{''}+9y=18t,y(0)=0,y^'(0)=0
y
′
′
+
9
y
=
1
8
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+2y^'-3y=3cos(x)
y
′
′
+
2
y
′
−
3
y
=
3
cos
(
x
)
y^{''}+4y^'+7=0
y
′
′
+
4
y
′
+
7
=
0
y^{''}+4y^'+2y=cos(2x)
y
′
′
+
4
y
′
+
2
y
=
cos
(
2
x
)
y^{''}+3y^'-4y=14e^x
y
′
′
+
3
y
′
−
4
y
=
1
4
e
x
(D^2+4D+4)y=xe^{-x}
(
D
2
+
4
D
+
4
)
y
=
xe
−
x
y^{''}-2y^'-3y=9t^2
y
′
′
−
2
y
′
−
3
y
=
9
t
2
y^{''}-3y^'-40y=(t+1)e^t
y
′
′
−
3
y
′
−
4
0
y
=
(
t
+
1
)
e
t
2y^{''}+5y^'+2y=xe^{-x}
2
y
′
′
+
5
y
′
+
2
y
=
xe
−
x
y^{''}-4y^'+4y=x^2*e^{2x}-e^{2x}
y
′
′
−
4
y
′
+
4
y
=
x
2
·
e
2
x
−
e
2
x
y^{''}+0.7y+4=cos(3t)
y
′
′
+
0
.
7
y
+
4
=
cos
(
3
t
)
y^{''}-4y^'+3y=e^{2t}
y
′
′
−
4
y
′
+
3
y
=
e
2
t
y^{''}+y^'=-16cos(3x)
y
′
′
+
y
′
=
−
1
6
cos
(
3
x
)
1y^{''}+5y^'+1/(1/6)y=2e^{2t}
1
y
′
′
+
5
y
′
+
1
1
6
y
=
2
e
2
t
y^{''}+2y^'-2y=5sin(x)-10xe^x
y
′
′
+
2
y
′
−
2
y
=
5
sin
(
x
)
−
1
0
xe
x
y^{''}-8y^'+17y=-102,y(0)=-3,y^'(0)=8
y
′
′
−
8
y
′
+
1
7
y
=
−
1
0
2
,
y
(
0
)
=
−
3
,
y
′
(
0
)
=
8
y^{''}-6y^'+9y=e^3xln(x)
y
′
′
−
6
y
′
+
9
y
=
e
3
x
ln
(
x
)
y^{'''}+2y^{''}+4y^'+8=0
y
′
′
′
+
2
y
′
′
+
4
y
′
+
8
=
0
y^{''''}-16y^{''}=x^2+e^{2x}
y
′
′
′
′
−
1
6
y
′
′
=
x
2
+
e
2
x
y^{''}-4y=sin(3t)
y
′
′
−
4
y
=
sin
(
3
t
)
y^{''}-9y=4-30x^2+9x^4
y
′
′
−
9
y
=
4
−
3
0
x
2
+
9
x
4
(d^2y)/(dx^2)+y=sec^2(x)
d
2
y
dx
2
+
y
=
sec
2
(
x
)
y^{''}+6y^'+9y=e^{-x}cos(2x)
y
′
′
+
6
y
′
+
9
y
=
e
−
x
cos
(
2
x
)
(d^2y)/(dx^2)-4(dy)/(dx)+13y=5cos(2x)
d
2
y
dx
2
−
4
dy
dx
+
1
3
y
=
5
cos
(
2
x
)
1
..
2363
2364
2365
2366
2367
..
2459