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일반적인 미적분학 문제
y^{'''}-6y^{''}+11y^'-6y=-1
y
′
′
′
−
6
y
′
′
+
1
1
y
′
−
6
y
=
−
1
4y^{''}+ky=8sin(t)
4
y
′
′
+
ky
=
8
sin
(
t
)
y^{''}-2y^'=xe^{2x}+x
y
′
′
−
2
y
′
=
xe
2
x
+
x
y^{''}-4y^'+4y=t^3*e^{2t}
y
′
′
−
4
y
′
+
4
y
=
t
3
·
e
2
t
y^{'''}+2y^{''}-y^'-2y=e^x+x^2
y
′
′
′
+
2
y
′
′
−
y
′
−
2
y
=
e
x
+
x
2
(d^2y)/(dx^2)-(dy)/(dx)+6x=0
d
2
y
dx
2
−
dy
dx
+
6
x
=
0
y^{''}-4y^'+4y=(1+x)e^{2x}
y
′
′
−
4
y
′
+
4
y
=
(
1
+
x
)
e
2
x
2y^{''}+y^'-y=1,y^'(0)=0
2
y
′
′
+
y
′
−
y
=
1
,
y
′
(
0
)
=
0
y^{''}-3y^'+2y=e^3x
y
′
′
−
3
y
′
+
2
y
=
e
3
x
2y^{''}-y^'-y=3e^x+2e^{-x}
2
y
′
′
−
y
′
−
y
=
3
e
x
+
2
e
−
x
y^{''}+2y^'+y=t^{(-1)}e^{(-t)}
y
′
′
+
2
y
′
+
y
=
t
(
−
1
)
e
(
−
t
)
y^{''}-y^'-6y=2e^{3t},y(0)=3,y^'(0)=1
y
′
′
−
y
′
−
6
y
=
2
e
3
t
,
y
(
0
)
=
3
,
y
′
(
0
)
=
1
y^{''}+6y^'=5x
y
′
′
+
6
y
′
=
5
x
(D^2+2D-3)y=cos(2x)
(
D
2
+
2
D
−
3
)
y
=
cos
(
2
x
)
y^{''}-8y^'=6e^{2x}-6x^2-9x-14
y
′
′
−
8
y
′
=
6
e
2
x
−
6
x
2
−
9
x
−
1
4
y^{''}+10y^'+41=0
y
′
′
+
1
0
y
′
+
4
1
=
0
y^{''}-3y^'+4y=16x-50cos(2x)
y
′
′
−
3
y
′
+
4
y
=
1
6
x
−
5
0
cos
(
2
x
)
y^{''}-y^'-3y-4=0
y
′
′
−
y
′
−
3
y
−
4
=
0
x^{''}+0.2x^'-x=0.3cos(1t)
x
′
′
+
0
.
2
x
′
−
x
=
0
.
3
cos
(
1
t
)
y^{''}-8y^'+16y=xe^{4x}
y
′
′
−
8
y
′
+
1
6
y
=
xe
4
x
(d^2-4d+3)y=2xe^{3x}+3e^xcos(2x)
(
d
2
−
4
d
+
3
)
y
=
2
xe
3
x
+
3
e
x
cos
(
2
x
)
x^{''}+6x^'+23x=8cos(4t)
x
′
′
+
6
x
′
+
2
3
x
=
8
cos
(
4
t
)
y^{''}-7y^'+12y=4e^x
y
′
′
−
7
y
′
+
1
2
y
=
4
e
x
y^{''}+3y=x^2sin(x)
y
′
′
+
3
y
=
x
2
sin
(
x
)
4y^{''}+36y=csc(x)
4
y
′
′
+
3
6
y
=
csc
(
x
)
y^{''}-2y^'+y=xe^x+4,y(0)=1,y^'(0)=1
y
′
′
−
2
y
′
+
y
=
xe
x
+
4
,
y
(
0
)
=
1
,
y
′
(
0
)
=
1
y^{''}-6y=u^2(t),y(0)=0
y
′
′
−
6
y
=
u
2
(
t
)
,
y
(
0
)
=
0
y^{''}+16y=e^{5t}
y
′
′
+
1
6
y
=
e
5
t
y^{''}+256y=16cos(3x)
y
′
′
+
2
5
6
y
=
1
6
cos
(
3
x
)
D(x)=-6(2940)+4200
D
(
x
)
=
−
6
(
2
9
4
0
)
+
4
2
0
0
y^{''''}-16y=2e^{-2x}+3e^{3x}+cos(2x)-1
y
′
′
′
′
−
1
6
y
=
2
e
−
2
x
+
3
e
3
x
+
cos
(
2
x
)
−
1
(d^2)/(dt^2)(θ(t))+4θ(t)=cos(c^2)(2t)
d
2
dt
2
(
θ
(
t
)
)
+
4
θ
(
t
)
=
cos
(
c
2
)
(
2
t
)
(d^2x)/(dt^2)+100x=36cos(8t)
d
2
x
dt
2
+
1
0
0
x
=
3
6
cos
(
8
t
)
y^{''}-6y^'+9y=t^{-7}e^{3t}
y
′
′
−
6
y
′
+
9
y
=
t
−
7
e
3
t
x^{''}+2x^'-4x=6e^{3t}-4t+3
x
′
′
+
2
x
′
−
4
x
=
6
e
3
t
−
4
t
+
3
y^{''}+4y^'+5y=3t+e^t
y
′
′
+
4
y
′
+
5
y
=
3
t
+
e
t
y^{''}-25y=3x^2-2+e^x,y(0)=1,y^'(0)=0
y
′
′
−
2
5
y
=
3
x
2
−
2
+
e
x
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
y^{''}-4y=8e^{2x},y(0)=1,y^'(0)=0
y
′
′
−
4
y
=
8
e
2
x
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
y^{''}+4y^'+40y=25sin(6t)
y
′
′
+
4
y
′
+
4
0
y
=
2
5
sin
(
6
t
)
x^2y^{''}-8x^2y^'+16x^2y=3e^{4x}
x
2
y
′
′
−
8
x
2
y
′
+
1
6
x
2
y
=
3
e
4
x
y^{''}+3y^'+2y=12e^t,y(0)=2,y^'(0)=3
y
′
′
+
3
y
′
+
2
y
=
1
2
e
t
,
y
(
0
)
=
2
,
y
′
(
0
)
=
3
y^{''}+4y^'+3y=4x^2+5
y
′
′
+
4
y
′
+
3
y
=
4
x
2
+
5
y^{''}-y^'-6y=73cos(3x)
y
′
′
−
y
′
−
6
y
=
7
3
cos
(
3
x
)
y^{'''}+y^{''}+y^'+y=e^{-t}+8t
y
′
′
′
+
y
′
′
+
y
′
+
y
=
e
−
t
+
8
t
y^{'''}+y^{''}+y^'+y=e^{-t}+7t
y
′
′
′
+
y
′
′
+
y
′
+
y
=
e
−
t
+
7
t
y^{''}-2y^'+y=6t-2,y(-1)=3,y^'(-1)=7
y
′
′
−
2
y
′
+
y
=
6
t
−
2
,
y
(
−
1
)
=
3
,
y
′
(
−
1
)
=
7
y^{''}+4y^'+y=4,y(0)=0,y^'(0)=1
y
′
′
+
4
y
′
+
y
=
4
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{''}-4y^'+5y=e^{2x}(sin(x)+2cos(x))
y
′
′
−
4
y
′
+
5
y
=
e
2
x
(
sin
(
x
)
+
2
cos
(
x
)
)
y^{''}-3y^'+5y=24e^{-2x}
y
′
′
−
3
y
′
+
5
y
=
2
4
e
−
2
x
x^{''}+5x^'+6x=2e^{-t}
x
′
′
+
5
x
′
+
6
x
=
2
e
−
t
y^{''}+y^'-2y=2xe^{2x}
y
′
′
+
y
′
−
2
y
=
2
xe
2
x
y^{''}-5y^'+6y=g(t)
y
′
′
−
5
y
′
+
6
y
=
g
(
t
)
2y^{''}-4y^'+4y=e^x*sec(x)
2
y
′
′
−
4
y
′
+
4
y
=
e
x
·
sec
(
x
)
(d^2y)/(dx^2)+4(dy)/(dx)+6y=1+e^{-x}
d
2
y
dx
2
+
4
dy
dx
+
6
y
=
1
+
e
−
x
y^{''}-7y^'+12=0
y
′
′
−
7
y
′
+
1
2
=
0
y^{''}-2y^'-3=0
y
′
′
−
2
y
′
−
3
=
0
y^{''}+4y^'+13y=5
y
′
′
+
4
y
′
+
1
3
y
=
5
y^{''}+4y^'+y=2
y
′
′
+
4
y
′
+
y
=
2
y^{''}+5y^'+6y=20te^{5t}
y
′
′
+
5
y
′
+
6
y
=
2
0
te
5
t
y^{''}-6y^'+8y=-3e^{2x}-5xe^{-4x}+3x
y
′
′
−
6
y
′
+
8
y
=
−
3
e
2
x
−
5
xe
−
4
x
+
3
x
y^{''''}-y^{''}=3x^2-2x
y
′
′
′
′
−
y
′
′
=
3
x
2
−
2
x
y^{'''}-2y^{''}+y^'=1
y
′
′
′
−
2
y
′
′
+
y
′
=
1
1/6 y^{''}+6y=tan(6x)-1/3 e^{3x}
1
6
y
′
′
+
6
y
=
tan
(
6
x
)
−
1
3
e
3
x
y^{''}-3y^'+2y=cos(2x)
y
′
′
−
3
y
′
+
2
y
=
cos
(
2
x
)
y^{'''}-y^'=10cos(2x)
y
′
′
′
−
y
′
=
1
0
cos
(
2
x
)
y^{''}+2y^'+2y=x^3-1
y
′
′
+
2
y
′
+
2
y
=
x
3
−
1
y^{''}-2y^'=x^2+2
y
′
′
−
2
y
′
=
x
2
+
2
x^{''}+2x^'+5x=8cos(2t)+2sin(2t)
x
′
′
+
2
x
′
+
5
x
=
8
cos
(
2
t
)
+
2
sin
(
2
t
)
y^{''}-y=e^{(2x)}
y
′
′
−
y
=
e
(
2
x
)
y^{''}+16y=7sin(x)
y
′
′
+
1
6
y
=
7
sin
(
x
)
y^{'''}-y^{''}-9y^'+9y=7-e^x+e^{3x}
y
′
′
′
−
y
′
′
−
9
y
′
+
9
y
=
7
−
e
x
+
e
3
x
3y^{''}-y=e^x-5
3
y
′
′
−
y
=
e
x
−
5
y^{''}+4y^'+4y=375*t
y
′
′
+
4
y
′
+
4
y
=
3
7
5
·
t
y^{''}-2y^'-15y=4e^t
y
′
′
−
2
y
′
−
1
5
y
=
4
e
t
y^{'''}+3y^{''}+2y^'=u
y
′
′
′
+
3
y
′
′
+
2
y
′
=
u
y^{''}-2y^'+2y=2x^2-2x+1+sin(x)
y
′
′
−
2
y
′
+
2
y
=
2
x
2
−
2
x
+
1
+
sin
(
x
)
y^{''}-y+3=0
y
′
′
−
y
+
3
=
0
y^{''}+4y^'+4y=3x+6
y
′
′
+
4
y
′
+
4
y
=
3
x
+
6
y^{''}-2y^'-8y=3e^{3x}
y
′
′
−
2
y
′
−
8
y
=
3
e
3
x
y^{''}+3y^'-5y=(4x^2-7x+0)e^{4x}
y
′
′
+
3
y
′
−
5
y
=
(
4
x
2
−
7
x
+
0
)
e
4
x
y^{''}-2y^'+y=4x^2-6
y
′
′
−
2
y
′
+
y
=
4
x
2
−
6
y^{''''}-2y^{''}+y=5sin(2x)
y
′
′
′
′
−
2
y
′
′
+
y
=
5
sin
(
2
x
)
y^{''}+3y=e^t
y
′
′
+
3
y
=
e
t
y^{''}-9y^'=9xe^{-3x}
y
′
′
−
9
y
′
=
9
xe
−
3
x
6y^{''}-15y^'=3x^2
6
y
′
′
−
1
5
y
′
=
3
x
2
y^{''}+14y^'+49y=t-2e-7t
y
′
′
+
1
4
y
′
+
4
9
y
=
t
−
2
e
−
7
t
y^{''}+9y=(x^2+1)e^{3x}
y
′
′
+
9
y
=
(
x
2
+
1
)
e
3
x
y^{''}+3y^'+2y=e^{-x}sin(2x)
y
′
′
+
3
y
′
+
2
y
=
e
−
x
sin
(
2
x
)
3x^{''}+12x=sin(2t)
3
x
′
′
+
1
2
x
=
sin
(
2
t
)
y^{''}+25y=2sin(2x),y(0)=1,y^'(0)=0
y
′
′
+
2
5
y
=
2
sin
(
2
x
)
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
y^{'''}+2y^{''}=12x+4
y
′
′
′
+
2
y
′
′
=
1
2
x
+
4
y^{''}+25y=25sec^2(5t)
y
′
′
+
2
5
y
=
2
5
sec
2
(
5
t
)
x''+2x=8,x(pi)=0,x(0)=0
x
′
′
+
2
x
=
8
,
x
(
π
)
=
0
,
x
(
0
)
=
0
y^{''}-y^'-42y=-122t+84t^2
y
′
′
−
y
′
−
4
2
y
=
−
1
2
2
t
+
8
4
t
2
(d^2y)/(dt^2)+12(dy)/(dt)+36y=-4t+3
d
2
y
dt
2
+
1
2
dy
dt
+
3
6
y
=
−
4
t
+
3
y^{''}-2y^'=4x+e^x
y
′
′
−
2
y
′
=
4
x
+
e
x
y^{''}+2y^'=cos(t),y(0)=0
y
′
′
+
2
y
′
=
cos
(
t
)
,
y
(
0
)
=
0
y^{''}+7y^'=cos(2x)+8e^{-5x}
y
′
′
+
7
y
′
=
cos
(
2
x
)
+
8
e
−
5
x
y^{''}+3y^'-4y=2,y^'(0)=0,y(0)=0
y
′
′
+
3
y
′
−
4
y
=
2
,
y
′
(
0
)
=
0
,
y
(
0
)
=
0
y^{''}-3y^'-4y=3e^2t+2sin(t)
y
′
′
−
3
y
′
−
4
y
=
3
e
2
t
+
2
sin
(
t
)
1
..
2364
2365
2366
2367
2368
..
2459