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일반적인 미적분학 문제
x^{''}+4x^'+3x=1,x^'(0)=0
x
′
′
+
4
x
′
+
3
x
=
1
,
x
′
(
0
)
=
0
y^{'''}+y^'=sec(t),y^{'''}(0)=-2
y
′
′
′
+
y
′
=
sec
(
t
)
,
y
′
′
′
(
0
)
=
−
2
(d^2y)/(dx^2)+y=2e^{3x}
d
2
y
dx
2
+
y
=
2
e
3
x
y^{'''}-y^{''}-4y^'+4y=10e^{3t}
y
′
′
′
−
y
′
′
−
4
y
′
+
4
y
=
1
0
e
3
t
y^{''}-4y^'+4y=4xln(x)
y
′
′
−
4
y
′
+
4
y
=
4
x
ln
(
x
)
(d^2-4d+3)y=e^{3x}cos(x)
(
d
2
−
4
d
+
3
)
y
=
e
3
x
cos
(
x
)
y^{''}-4y^'+4y=4t^2-4t+26
y
′
′
−
4
y
′
+
4
y
=
4
t
2
−
4
t
+
2
6
y^{''}+(y^')/2-y/2 =(x+1)/2
y
′
′
+
y
′
2
−
y
2
=
x
+
1
2
y^{''}+y^'=tan(t)
y
′
′
+
y
′
=
tan
(
t
)
x^{''}-2x^'+2x=t
x
′
′
−
2
x
′
+
2
x
=
t
y^{''}-4y^'-2y=2e^{-3t},y(0)=1,y^'(0)=7
y
′
′
−
4
y
′
−
2
y
=
2
e
−
3
t
,
y
(
0
)
=
1
,
y
′
(
0
)
=
7
y^{''}+4y^'+12y=4x^2
y
′
′
+
4
y
′
+
1
2
y
=
4
x
2
y^{'''}-9y^{''}+27y^'-27y=9e^{3x}
y
′
′
′
−
9
y
′
′
+
2
7
y
′
−
2
7
y
=
9
e
3
x
y^{''}+6y^'+5y=t*e^{-t}
y
′
′
+
6
y
′
+
5
y
=
t
·
e
−
t
y^{''}-6y^'-16y=-24t+32t^2
y
′
′
−
6
y
′
−
1
6
y
=
−
2
4
t
+
3
2
t
2
16y^{''}+y=4sec(pi/4)
1
6
y
′
′
+
y
=
4
sec
(
π
4
)
y^{''}-2y^'+y=e^{3x}
y
′
′
−
2
y
′
+
y
=
e
3
x
y^{''}+y^'-8y=48t
y
′
′
+
y
′
−
8
y
=
4
8
t
y^{''}-2y^'+1=xe^x
y
′
′
−
2
y
′
+
1
=
xe
x
y^{''}+y^'-6y=6e^{2x}
y
′
′
+
y
′
−
6
y
=
6
e
2
x
y^{''}-2y^'-3y=4e^x-9+24x+4
y
′
′
−
2
y
′
−
3
y
=
4
e
x
−
9
+
2
4
x
+
4
y^{''''}-2y^{''}+1=0
y
′
′
′
′
−
2
y
′
′
+
1
=
0
x^{''}+b*x^'+a=0
x
′
′
+
b
·
x
′
+
a
=
0
x^{''}-6x-16x=sin(2t)
x
′
′
−
6
x
−
1
6
x
=
sin
(
2
t
)
y^{''}+4y=x^2+5e^x
y
′
′
+
4
y
=
x
2
+
5
e
x
y^{'''}+y=e^{-x}
y
′
′
′
+
y
=
e
−
x
y^{''}+6y^'+3x=0,y(0)=0,y^'(0)=1
y
′
′
+
6
y
′
+
3
x
=
0
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{''}+5y=5sin(x),y(0)=1,y^'(0)=2
y
′
′
+
5
y
=
5
sin
(
x
)
,
y
(
0
)
=
1
,
y
′
(
0
)
=
2
y^{'''}+y^'=sec(t),y^'(0)=3,y^{''}(0)=-2
y
′
′
′
+
y
′
=
sec
(
t
)
,
y
′
(
0
)
=
3
,
y
′
′
(
0
)
=
−
2
(d^2y)/(dx^2)-2*(dy)/(dx)+y=(x-1)*e^x
d
2
y
dx
2
−
2
·
dy
dx
+
y
=
(
x
−
1
)
·
e
x
(d^2y)/(dx^2)+(dy)/(dx)=sin(x)
d
2
y
dx
2
+
dy
dx
=
sin
(
x
)
y^{''}-81y=e^{9x}
y
′
′
−
8
1
y
=
e
9
x
x^{''}-4x^'+3x=2e^t-5e^{2t}
x
′
′
−
4
x
′
+
3
x
=
2
e
t
−
5
e
2
t
y^{''}+4y=t^2+7e^t,y(0)=0,y^'(0)=2
y
′
′
+
4
y
=
t
2
+
7
e
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
2
y^{''}+y^'=(3t^2+2t)e^t+cos(t/2)
y
′
′
+
y
′
=
(
3
t
2
+
2
t
)
e
t
+
cos
(
t
2
)
y^{''}+5y^'-6y=2sin(4x)
y
′
′
+
5
y
′
−
6
y
=
2
sin
(
4
x
)
y^{'''}+3y^{''}-9y^'+5y=4e^{-x}+cos(x)
y
′
′
′
+
3
y
′
′
−
9
y
′
+
5
y
=
4
e
−
x
+
cos
(
x
)
y^{''}+3y^'+4y=20x+33
y
′
′
+
3
y
′
+
4
y
=
2
0
x
+
3
3
y^{''}-2y^'+5y=cos(4x)+1
y
′
′
−
2
y
′
+
5
y
=
cos
(
4
x
)
+
1
x^{''}+x=5cos(t)
x
′
′
+
x
=
5
cos
(
t
)
y^{''}-2y^'+y=3
y
′
′
−
2
y
′
+
y
=
3
y^{''}+2y= 1/(cos(sqrt(2)x))
y
′
′
+
2
y
=
1
cos
(
√
2
x
)
y^{''}-4y^'+4y=t^{-3}e^{2t}
y
′
′
−
4
y
′
+
4
y
=
t
−
3
e
2
t
y^{''}+4y^'-32=0
y
′
′
+
4
y
′
−
3
2
=
0
y^{''}+16y=e^{5t},y(0)=0,y^'(0)=0
y
′
′
+
1
6
y
=
e
5
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}-4y^'+4y=e^{2x}+x^2
y
′
′
−
4
y
′
+
4
y
=
e
2
x
+
x
2
y^{'''}+10y^{''}+25y^'=ex
y
′
′
′
+
1
0
y
′
′
+
2
5
y
′
=
ex
y^{''}-y^'+2y=x
y
′
′
−
y
′
+
2
y
=
x
2y^{''}+2y^'+2y=sin(t)+1
2
y
′
′
+
2
y
′
+
2
y
=
sin
(
t
)
+
1
u^{''}+au^'(t)=b
u
′
′
+
au
′
(
t
)
=
b
6y^{''}+3y^'-30y=16cos(x)
6
y
′
′
+
3
y
′
−
3
0
y
=
1
6
cos
(
x
)
y^{''}-5y^'-36y=e^{9x}
y
′
′
−
5
y
′
−
3
6
y
=
e
9
x
y^{''}+y^'+y=sin(x)+x+x^2-1
y
′
′
+
y
′
+
y
=
sin
(
x
)
+
x
+
x
2
−
1
y^{''}+y=e^{2x},y(0)=0
y
′
′
+
y
=
e
2
x
,
y
(
0
)
=
0
y^{''}-2y^'-3y=xe^{-x}
y
′
′
−
2
y
′
−
3
y
=
xe
−
x
x^{''}+x=2e^t
x
′
′
+
x
=
2
e
t
y^{'''}-3y^{''}+4y=12e^{2x}+4e^{3x}
y
′
′
′
−
3
y
′
′
+
4
y
=
1
2
e
2
x
+
4
e
3
x
y^{''}-4y^'+4y=2x^2+4xe^{2x}+xsin(2x)
y
′
′
−
4
y
′
+
4
y
=
2
x
2
+
4
xe
2
x
+
x
sin
(
2
x
)
y^{''}=x-y
y
′
′
=
x
−
y
y^{''}+y^'-12y=4,y(0)=0,y^'(0)=0
y
′
′
+
y
′
−
1
2
y
=
4
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}-3y^'=x
y
′
′
−
3
y
′
=
x
y^{''}+12y^'+100y=48sin(10t)
y
′
′
+
1
2
y
′
+
1
0
0
y
=
4
8
sin
(
1
0
t
)
x^{''}+25x=102cos(t)
x
′
′
+
2
5
x
=
1
0
2
cos
(
t
)
y^{''}-y^'=3-4x
y
′
′
−
y
′
=
3
−
4
x
y^{''}+3y+2y=cos(e^x)
y
′
′
+
3
y
+
2
y
=
cos
(
e
x
)
y^{''}+15y^'+7y=sin(x)+cos(x)
y
′
′
+
1
5
y
′
+
7
y
=
sin
(
x
)
+
cos
(
x
)
(y^{''})-2y^'+y=(e^x)/(1+x^2)
(
y
′
′
)
−
2
y
′
+
y
=
e
x
1
+
x
2
y^{''}+2y^'+2y=t^2
y
′
′
+
2
y
′
+
2
y
=
t
2
y^{''}-2y^'+y=e-2x
y
′
′
−
2
y
′
+
y
=
e
−
2
x
y^{''}-3y^'+5y=2e^t
y
′
′
−
3
y
′
+
5
y
=
2
e
t
y^{''}+4y^'+6y=1^{-t}
y
′
′
+
4
y
′
+
6
y
=
1
−
t
y^{''}+y=t-pi/2 ,y(pi/2)=0,y^'(pi/2)=1
y
′
′
+
y
=
t
−
π
2
,
y
(
π
2
)
=
0
,
y
′
(
π
2
)
=
1
y^{''}-y^'-2y=(x+1)e^{-x}
y
′
′
−
y
′
−
2
y
=
(
x
+
1
)
e
−
x
y^{''}-2y^'-3y=2
y
′
′
−
2
y
′
−
3
y
=
2
y^{''}+6y^'+9y=(e^{-3x})/((x^2+1))
y
′
′
+
6
y
′
+
9
y
=
e
−
3
x
(
x
2
+
1
)
y^{''}-2y^'-3y=-4e^x+3
y
′
′
−
2
y
′
−
3
y
=
−
4
e
x
+
3
y^{''}+y=sin(t)+cos(t)
y
′
′
+
y
=
sin
(
t
)
+
cos
(
t
)
y^{''}+2y^'+2y=xe^{-2x}+3x
y
′
′
+
2
y
′
+
2
y
=
xe
−
2
x
+
3
x
y^{''}-y^'-6y=12x-e^x
y
′
′
−
y
′
−
6
y
=
1
2
x
−
e
x
y^{''}+5y^'-4y=8t+8
y
′
′
+
5
y
′
−
4
y
=
8
t
+
8
y^{''}-8y^'+16y=e^x
y
′
′
−
8
y
′
+
1
6
y
=
e
x
d^2y=(2x^2+4)(x^2+3x)^4
d
2
y
=
(
2
x
2
+
4
)
(
x
2
+
3
x
)
4
(d^2y)/(dx^2)+3(dy)/(dx)-4y=x^2
d
2
y
dx
2
+
3
dy
dx
−
4
y
=
x
2
y^{''}+3y^'+2y=-6-4x-7x^2-2x^3
y
′
′
+
3
y
′
+
2
y
=
−
6
−
4
x
−
7
x
2
−
2
x
3
(D^2+1)y=12cos^2(x)
(
D
2
+
1
)
y
=
1
2
cos
2
(
x
)
(D^2+3D+2)y=1+3x+x^2
(
D
2
+
3
D
+
2
)
y
=
1
+
3
x
+
x
2
y^{''}-4y=cos(x)-sin(x)
y
′
′
−
4
y
=
cos
(
x
)
−
sin
(
x
)
y^{''}+8y^'+12y=xe^{2x}
y
′
′
+
8
y
′
+
1
2
y
=
xe
2
x
x^{''}+2x^'+1x=e^{-2t}
x
′
′
+
2
x
′
+
1
x
=
e
−
2
t
y^{''}+9y=4sin(3x)
y
′
′
+
9
y
=
4
sin
(
3
x
)
y^{''}+4y^'+4y=x^2*e^{-2x}+1
y
′
′
+
4
y
′
+
4
y
=
x
2
·
e
−
2
x
+
1
y^{''}+7y=5
y
′
′
+
7
y
=
5
x^{''}+x^'-2x=8sin(2t)
x
′
′
+
x
′
−
2
x
=
8
sin
(
2
t
)
y^{''}-5y^'+6y=(12x-7)e^{-x}
y
′
′
−
5
y
′
+
6
y
=
(
1
2
x
−
7
)
e
−
x
y^{''}+25y=20sin(5x)+xcos(x)
y
′
′
+
2
5
y
=
2
0
sin
(
5
x
)
+
x
cos
(
x
)
2y^{''}-13y^'+20y=40x^2+8x+10
2
y
′
′
−
1
3
y
′
+
2
0
y
=
4
0
x
2
+
8
x
+
1
0
y^{''}-2y^'+10y=20x,y(0)=0,y^'(0)=0
y
′
′
−
2
y
′
+
1
0
y
=
2
0
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
-ay^{''}+by-1=0
−
ay
′
′
+
by
−
1
=
0
y^{''}+16y=80t^2-96t+42,y(0)=0,y^'(0)=14
y
′
′
+
1
6
y
=
8
0
t
2
−
9
6
t
+
4
2
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
4
y^{'''}-24y^{''}+192y^'-512y=e^{8x}
y
′
′
′
−
2
4
y
′
′
+
1
9
2
y
′
−
5
1
2
y
=
e
8
x
1
..
2367
2368
2369
2370
2371
..
2459