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일반적인 미적분학 문제
y^{''}-y=2ln(x)
y
′
′
−
y
=
2
ln
(
x
)
y^{''}-2y^'+y=25cos(2x)
y
′
′
−
2
y
′
+
y
=
2
5
cos
(
2
x
)
(d^2y)/(dx^2)=ay+b
d
2
y
dx
2
=
ay
+
b
y^{''}+6y^'+5y=10cos(5t)
y
′
′
+
6
y
′
+
5
y
=
1
0
cos
(
5
t
)
y^{''}-4y^'-12y=sin(3t)
y
′
′
−
4
y
′
−
1
2
y
=
sin
(
3
t
)
(d^2y)/(dx^2)+9y=-15x+7+e^x
d
2
y
dx
2
+
9
y
=
−
1
5
x
+
7
+
e
x
y^{''}+9y=sin(3x)+e^{2x}
y
′
′
+
9
y
=
sin
(
3
x
)
+
e
2
x
y^{''}-y^'-2y=8x+5
y
′
′
−
y
′
−
2
y
=
8
x
+
5
y^{''}-2y^'-3y=2e^{3t}
y
′
′
−
2
y
′
−
3
y
=
2
e
3
t
y^{''}-4y^'+4y=e^2xln(x)
y
′
′
−
4
y
′
+
4
y
=
e
2
x
ln
(
x
)
y^{''}-8y^'-4y-2=10x^2-2xe^2
y
′
′
−
8
y
′
−
4
y
−
2
=
1
0
x
2
−
2
xe
2
y^{''}-y^'-6y=22cos(3x)
y
′
′
−
y
′
−
6
y
=
2
2
cos
(
3
x
)
9y^{''}+6y^'+y=2,y(0)=0,y^'(0)=0
9
y
′
′
+
6
y
′
+
y
=
2
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}-4y^'+4y=t
y
′
′
−
4
y
′
+
4
y
=
t
y^{''''}+4y^{''}=sin(2t)+te^{3t}+4
y
′
′
′
′
+
4
y
′
′
=
sin
(
2
t
)
+
te
3
t
+
4
y^{''}-y^'-12=0
y
′
′
−
y
′
−
1
2
=
0
y^{'''}+y=sin(x)
y
′
′
′
+
y
=
sin
(
x
)
y^{''}+4y=g(t),y(0)=4,y^'(0)=0
y
′
′
+
4
y
=
g
(
t
)
,
y
(
0
)
=
4
,
y
′
(
0
)
=
0
y^{''}-3+y^'+2y=0
y
′
′
−
3
+
y
′
+
2
y
=
0
y^{''}-4y=4x
y
′
′
−
4
y
=
4
x
x^{''}+2x^'+151x=8cos(12t)
x
′
′
+
2
x
′
+
1
5
1
x
=
8
cos
(
1
2
t
)
y^{''}+3y=-48t^2e^3t
y
′
′
+
3
y
=
−
4
8
t
2
e
3
t
y^{''''}-256y=2e^{-4x}+3e^{3x}+cos(4x)+2
y
′
′
′
′
−
2
5
6
y
=
2
e
−
4
x
+
3
e
3
x
+
cos
(
4
x
)
+
2
y^{''}+y=3e^{-6x},y(0)=0,y^'(0)=0
y
′
′
+
y
=
3
e
−
6
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
(D^2-2D+1)y=e^{2x}(e^x+1)^{-2}
(
D
2
−
2
D
+
1
)
y
=
e
2
x
(
e
x
+
1
)
−
2
y^{''}-6y^'+9y=t^2e^3t
y
′
′
−
6
y
′
+
9
y
=
t
2
e
3
t
y^{''}-10y^'+25y=132x^2(e^{(5x)})
y
′
′
−
1
0
y
′
+
2
5
y
=
1
3
2
x
2
(
e
(
5
x
)
)
y^{''}-2y=e^{2x}+x^2-1
y
′
′
−
2
y
=
e
2
x
+
x
2
−
1
y^{''}-3y^'=2e^{2x}sin(x)
y
′
′
−
3
y
′
=
2
e
2
x
sin
(
x
)
y^{''}+y^'+y=e^{-t}+sin(2t)
y
′
′
+
y
′
+
y
=
e
−
t
+
sin
(
2
t
)
x^{''}+4x=32sin(4t)
x
′
′
+
4
x
=
3
2
sin
(
4
t
)
(D^2-2D-1)y=e^xcos(x)
(
D
2
−
2
D
−
1
)
y
=
e
x
cos
(
x
)
선의 (d^2x)/(dt^2)+x=6cos(2t)
linear
d
2
x
dt
2
+
x
=
6
cos
(
2
t
)
y^{''}+2y^'+5y=e^{-x}
y
′
′
+
2
y
′
+
5
y
=
e
−
x
y^{''}+4y^'+4y=4x^2-8x
y
′
′
+
4
y
′
+
4
y
=
4
x
2
−
8
x
y^{''}+y=(sec(x))^3
y
′
′
+
y
=
(
sec
(
x
)
)
3
y^{''}-2y^'-3y=3xe^{2x},y(0)=1,y^'(0)=0
y
′
′
−
2
y
′
−
3
y
=
3
xe
2
x
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
y^{''}+3y^'=x
y
′
′
+
3
y
′
=
x
y^{'''}+3y^{''}+3y^'+y=sqrt(x)e^{-x}
y
′
′
′
+
3
y
′
′
+
3
y
′
+
y
=
√
x
e
−
x
y^{''}-12y^'+36y=18e^{6x}
y
′
′
−
1
2
y
′
+
3
6
y
=
1
8
e
6
x
y^{''}-5y^'-6y=e^x
y
′
′
−
5
y
′
−
6
y
=
e
x
x^{''}+3x^'+2x=1,x(0)=0
x
′
′
+
3
x
′
+
2
x
=
1
,
x
(
0
)
=
0
y^{'''}-3y^{''}+2y^'=(e^{2x})/(1+e^x)
y
′
′
′
−
3
y
′
′
+
2
y
′
=
e
2
x
1
+
e
x
y^{''}+y^'=(3t^2+2t)e^t
y
′
′
+
y
′
=
(
3
t
2
+
2
t
)
e
t
(d^2y)/(dx^2)+4y=3sin(2x)
d
2
y
dx
2
+
4
y
=
3
sin
(
2
x
)
y^{''}+4y=5e^x-4x^2
y
′
′
+
4
y
=
5
e
x
−
4
x
2
y^{''}+x+y=0
y
′
′
+
x
+
y
=
0
y^{''}+y=1,y(0)=0,y(1)=0
y
′
′
+
y
=
1
,
y
(
0
)
=
0
,
y
(
1
)
=
0
y^{''}+12y^'+27y=64e^{-1t}
y
′
′
+
1
2
y
′
+
2
7
y
=
6
4
e
−
1
t
y^{''}+4y=4*sec^2(2t)
y
′
′
+
4
y
=
4
·
sec
2
(
2
t
)
2y^{''}-6y^'=5,y(0)=2,y^'(0)=1
2
y
′
′
−
6
y
′
=
5
,
y
(
0
)
=
2
,
y
′
(
0
)
=
1
y^{''}+y=1,y(0)=1,y^'(0)=1
y
′
′
+
y
=
1
,
y
(
0
)
=
1
,
y
′
(
0
)
=
1
y^{''}+5y^'+6y=1,y(0)=1,y^'(0)=0
y
′
′
+
5
y
′
+
6
y
=
1
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
y^{''}+25y=17sec^2(5t)
y
′
′
+
2
5
y
=
1
7
sec
2
(
5
t
)
y^{''}+y^'-6y=3x-2
y
′
′
+
y
′
−
6
y
=
3
x
−
2
y^{''}-16y^'+64y=2e^{8x}
y
′
′
−
1
6
y
′
+
6
4
y
=
2
e
8
x
y^{''}+9y=9sec(3t)
y
′
′
+
9
y
=
9
sec
(
3
t
)
y^{''}-y^'+81y=9sin(9t)
y
′
′
−
y
′
+
8
1
y
=
9
sin
(
9
t
)
y^{''}+4y=16t,y^0=3,y^'0=-6
y
′
′
+
4
y
=
1
6
t
,
y
0
=
3
,
y
′
0
=
−
6
y^{''}+3y^'+2y=e^{-2x}+x^2
y
′
′
+
3
y
′
+
2
y
=
e
−
2
x
+
x
2
y^{''}-7y=t^2
y
′
′
−
7
y
=
t
2
(y^{''}+2y^'+5)=e^x
(
y
′
′
+
2
y
′
+
5
)
=
e
x
y^{'''}+y^'=x+sin(x)+cos(x)
y
′
′
′
+
y
′
=
x
+
sin
(
x
)
+
cos
(
x
)
y^{''}+y^'-2y=3e^{-2x}-2x
y
′
′
+
y
′
−
2
y
=
3
e
−
2
x
−
2
x
y^{''}+y^'-2y=2t,y(0)=0
y
′
′
+
y
′
−
2
y
=
2
t
,
y
(
0
)
=
0
y^{''}-3y^'+y=2e^x+e^{-x}
y
′
′
−
3
y
′
+
y
=
2
e
x
+
e
−
x
y^{''}+3y^'+2y=4e^x
y
′
′
+
3
y
′
+
2
y
=
4
e
x
2y^{''}+4y^'+2y=e^{2x}cos(2x)
2
y
′
′
+
4
y
′
+
2
y
=
e
2
x
cos
(
2
x
)
x^{''}-x=1
x
′
′
−
x
=
1
2y^{''}-4y^'+4y=e^xtan(x)sec(x)
2
y
′
′
−
4
y
′
+
4
y
=
e
x
tan
(
x
)
sec
(
x
)
x^{''}+49x=99cos(4t)
x
′
′
+
4
9
x
=
9
9
cos
(
4
t
)
y^{''}-8y^'+20y=100x^2-65
y
′
′
−
8
y
′
+
2
0
y
=
1
0
0
x
2
−
6
5
y^{''}+2y^'-8y=4e^{-2x}-e^{-x}
y
′
′
+
2
y
′
−
8
y
=
4
e
−
2
x
−
e
−
x
y^{''}-4y^'+4y=(x+1)*e^{2x}
y
′
′
−
4
y
′
+
4
y
=
(
x
+
1
)
·
e
2
x
y^{''}+6y^'+13y=10e^{-2t},y(0)=3
y
′
′
+
6
y
′
+
1
3
y
=
1
0
e
−
2
t
,
y
(
0
)
=
3
4y^{''}+y=sin(t),y(0)=0,y^'(0)=1
4
y
′
′
+
y
=
sin
(
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{''}+16y=cos(4x)+sin(4x),y^0=3,y^'0=5
y
′
′
+
1
6
y
=
cos
(
4
x
)
+
sin
(
4
x
)
,
y
0
=
3
,
y
′
0
=
5
y^{'''}+289y^'=tan(17x)
y
′
′
′
+
2
8
9
y
′
=
tan
(
1
7
x
)
y^{''}-3y^'-4y=t^2
y
′
′
−
3
y
′
−
4
y
=
t
2
y^{''}+y=5cos(x),y(0)=0,y(0)=1
y
′
′
+
y
=
5
cos
(
x
)
,
y
(
0
)
=
0
,
y
(
0
)
=
1
y^{''}-2y^'+y=2e^t,y(0)=1,y^'(0)=1
y
′
′
−
2
y
′
+
y
=
2
e
t
,
y
(
0
)
=
1
,
y
′
(
0
)
=
1
x^{''}-x^'-6x=5t
x
′
′
−
x
′
−
6
x
=
5
t
y^{'''}-3y^{''}+3y^'-y=x-7ex
y
′
′
′
−
3
y
′
′
+
3
y
′
−
y
=
x
−
7
ex
y^{''}-2y^'-3y=8e^{-t}
y
′
′
−
2
y
′
−
3
y
=
8
e
−
t
y^{''}-y^'+4y=x^3e^{2x}+xe^{2x}
y
′
′
−
y
′
+
4
y
=
x
3
e
2
x
+
xe
2
x
y^{''}-2y^'=2+e^{2x}
y
′
′
−
2
y
′
=
2
+
e
2
x
9y^{''}+6y^'+y=x^2
9
y
′
′
+
6
y
′
+
y
=
x
2
y^{''}+10y^'+26y=2e^{-5x}cos(x)
y
′
′
+
1
0
y
′
+
2
6
y
=
2
e
−
5
x
cos
(
x
)
(D^2+3D+2)y=40e^{3x}
(
D
2
+
3
D
+
2
)
y
=
4
0
e
3
x
y^{''}-y^'-6y=sin(3x)
y
′
′
−
y
′
−
6
y
=
sin
(
3
x
)
y^{'''}-y^'=2cos(x)
y
′
′
′
−
y
′
=
2
cos
(
x
)
y^{'''}-5y^{''}+8y^'-4y=e^{2x}-4x+4
y
′
′
′
−
5
y
′
′
+
8
y
′
−
4
y
=
e
2
x
−
4
x
+
4
y^{''}-y^'-2y=15x+9
y
′
′
−
y
′
−
2
y
=
1
5
x
+
9
y^{''}-y^'-2y=15x+8
y
′
′
−
y
′
−
2
y
=
1
5
x
+
8
y^{''}+6y^'+25y=15cos(5t)
y
′
′
+
6
y
′
+
2
5
y
=
1
5
cos
(
5
t
)
y^{''}-4y^'+4y=2t^6e^{2t}
y
′
′
−
4
y
′
+
4
y
=
2
t
6
e
2
t
y^{''}-2y^'+y=t^{-7}e^t
y
′
′
−
2
y
′
+
y
=
t
−
7
e
t
y^{''}-y-2=0,y(0)=3
y
′
′
−
y
−
2
=
0
,
y
(
0
)
=
3
y^{''}-6y^'+8y=2
y
′
′
−
6
y
′
+
8
y
=
2
y^{''}+3y^'-4=0
y
′
′
+
3
y
′
−
4
=
0
1
..
2347
2348
2349
2350
2351
..
2459