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일반적인 미적분학 문제
y^{''}+4y=e^{3t},y(0)=0,y^'(0)=0
y
′
′
+
4
y
=
e
3
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+a^2y=cos(bt)
y
′
′
+
a
2
y
=
cos
(
bt
)
y^{''}-12y^'+36y=7+2x
y
′
′
−
1
2
y
′
+
3
6
y
=
7
+
2
x
y^{''}-2y^'+y=e^2x
y
′
′
−
2
y
′
+
y
=
e
2
x
y^{''}-3y=cos(3x)
y
′
′
−
3
y
=
cos
(
3
x
)
y^{''}-4y=4t-8e^{-2t}
y
′
′
−
4
y
=
4
t
−
8
e
−
2
t
y^{''}+y^'=cos(3t),y(0)=0,y^'(0)=1
y
′
′
+
y
′
=
cos
(
3
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{''}+8y^'+16y=(3e^{-4x})/(x^4)
y
′
′
+
8
y
′
+
1
6
y
=
3
e
−
4
x
x
4
y^{''}-2y^'-3y=4,y^'(0)=-1
y
′
′
−
2
y
′
−
3
y
=
4
,
y
′
(
0
)
=
−
1
y^{''}+9y=cos(3t),y(0)=0,y^'(0)=0
y
′
′
+
9
y
=
cos
(
3
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+9y=-18
y
′
′
+
9
y
=
−
1
8
y^{''}-y=e^{3x}
y
′
′
−
y
=
e
3
x
1q^{''}+4q^'+5q=5cos(40t)
1
q
′
′
+
4
q
′
+
5
q
=
5
cos
(
4
0
t
)
y^{''}-2y^'-3y=12ex-3
y
′
′
−
2
y
′
−
3
y
=
1
2
ex
−
3
(d^3+10d^2+25d)y=e^x
(
d
3
+
1
0
d
2
+
2
5
d
)
y
=
e
x
y^{''''}+2y^{''}+y=11+cos(4t)
y
′
′
′
′
+
2
y
′
′
+
y
=
1
1
+
cos
(
4
t
)
2y^{''}+3y^'-2y=10x^2-4x-13
2
y
′
′
+
3
y
′
−
2
y
=
1
0
x
2
−
4
x
−
1
3
y^{''}+2y^'=te^{-t},y(0)=6,y^'(0)=-1
y
′
′
+
2
y
′
=
te
−
t
,
y
(
0
)
=
6
,
y
′
(
0
)
=
−
1
y^{''}-5y^'=3e^{5t}-7t+4
y
′
′
−
5
y
′
=
3
e
5
t
−
7
t
+
4
e^xy^{''}+2e^xy^'+e^xy=ln(x)
e
x
y
′
′
+
2
e
x
y
′
+
e
x
y
=
ln
(
x
)
y^{'''}+y^{''}=4x+e^{-x}
y
′
′
′
+
y
′
′
=
4
x
+
e
−
x
y^{''}-6y^'+9y=-12e^{3x}
y
′
′
−
6
y
′
+
9
y
=
−
1
2
e
3
x
2y^{''}+y^'=4x
2
y
′
′
+
y
′
=
4
x
y^{''}+y^'+y=2x
y
′
′
+
y
′
+
y
=
2
x
y^{''}-2y^'-3y=6-3e^{-x}+4cos(3x)
y
′
′
−
2
y
′
−
3
y
=
6
−
3
e
−
x
+
4
cos
(
3
x
)
y^{''}-y=e^2x
y
′
′
−
y
=
e
2
x
y^{''}-8y^'+5y=xe^x
y
′
′
−
8
y
′
+
5
y
=
xe
x
(d^2y)/(dt^2)+3(dy)/(dt)+5y=sin(t)
d
2
y
dt
2
+
3
dy
dt
+
5
y
=
sin
(
t
)
y^{''}-y=xe^{2x},y(0)=0,y^'(0)=1
y
′
′
−
y
=
xe
2
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
d(x)= 9/x
d
(
x
)
=
9
x
y^{''}+4y=t^2+10e^t,y(0)=0,y^'(0)=1
y
′
′
+
4
y
=
t
2
+
1
0
e
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{'''}+3y^{''}+3y^'+y=x^{-3}e^{-x}
y
′
′
′
+
3
y
′
′
+
3
y
′
+
y
=
x
−
3
e
−
x
y^{''}-y^'+12y=t,y(0)=1,y^'(0)=1
y
′
′
−
y
′
+
1
2
y
=
t
,
y
(
0
)
=
1
,
y
′
(
0
)
=
1
25y^{''}-y=xe^{1/5 x}
2
5
y
′
′
−
y
=
xe
1
5
x
3x^{''}+10x=2sin(3t)
3
x
′
′
+
1
0
x
=
2
sin
(
3
t
)
y^{''}-y^'-6y=(10x+7)e^{3x}
y
′
′
−
y
′
−
6
y
=
(
1
0
x
+
7
)
e
3
x
y^{''}-3y^'+2y=e^{4t}
y
′
′
−
3
y
′
+
2
y
=
e
4
t
y^{''}+4y^'+5y=e^{-x}+15x
y
′
′
+
4
y
′
+
5
y
=
e
−
x
+
1
5
x
x^{''}+9.8x=cos(2t)
x
′
′
+
9
.
8
x
=
cos
(
2
t
)
y^{''}+3y^'+2y=3sin(x)+4x
y
′
′
+
3
y
′
+
2
y
=
3
sin
(
x
)
+
4
x
y^{''}-6y^'+8y=2,y(0)=0,y^'(0)=0
y
′
′
−
6
y
′
+
8
y
=
2
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
x^{''}+49x=52cos(6t)
x
′
′
+
4
9
x
=
5
2
cos
(
6
t
)
y^{''}-3y^'+2y=-2x
y
′
′
−
3
y
′
+
2
y
=
−
2
x
y^{''}-5y^'+6y=12x-4
y
′
′
−
5
y
′
+
6
y
=
1
2
x
−
4
y^{''}-y=4e-x^1-e-2x
y
′
′
−
y
=
4
e
−
x
1
−
e
−
2
x
y^{''}-2y^'-3y=12e^{3x}
y
′
′
−
2
y
′
−
3
y
=
1
2
e
3
x
y^{''}+2y^'+2y=e^xcos(x)
y
′
′
+
2
y
′
+
2
y
=
e
x
cos
(
x
)
y^{''}+40y^'+625y=100cos(10t)
y
′
′
+
4
0
y
′
+
6
2
5
y
=
1
0
0
cos
(
1
0
t
)
2y^{''}-y^'-2y=2e^{-t}
2
y
′
′
−
y
′
−
2
y
=
2
e
−
t
y^{''}+4y=20e^t,y(0)=0,y^'(0)=2
y
′
′
+
4
y
=
2
0
e
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
2
y^{''}-y=4x+3
y
′
′
−
y
=
4
x
+
3
y^{''}-15y^'+54y=39+54x
y
′
′
−
1
5
y
′
+
5
4
y
=
3
9
+
5
4
x
x^{''}+3x^'+2x=1,x(0)=0,x^'(0)=0
x
′
′
+
3
x
′
+
2
x
=
1
,
x
(
0
)
=
0
,
x
′
(
0
)
=
0
y^{''}-9y=54t
y
′
′
−
9
y
=
5
4
t
y^{''}+10y^'+25y=(e^{-5x})/(x^6)
y
′
′
+
1
0
y
′
+
2
5
y
=
e
−
5
x
x
6
y^{''}-4y^'+8y=12xe^{2x}+6e^{2x}
y
′
′
−
4
y
′
+
8
y
=
1
2
xe
2
x
+
6
e
2
x
y^{''}+y=8xcos(x)
y
′
′
+
y
=
8
x
cos
(
x
)
(D^2-6D+9)y=x^2e^{2x}
(
D
2
−
6
D
+
9
)
y
=
x
2
e
2
x
y^{''}+2y^'+10=0,y(0)=-2,y^'(0)=0
y
′
′
+
2
y
′
+
1
0
=
0
,
y
(
0
)
=
−
2
,
y
′
(
0
)
=
0
4y^{''}+y=10cos(x)
4
y
′
′
+
y
=
1
0
cos
(
x
)
y^{''}+4y^'+4y=8e^{-2}x
y
′
′
+
4
y
′
+
4
y
=
8
e
−
2
x
y^{''}+3y^'+2y=2x+3
y
′
′
+
3
y
′
+
2
y
=
2
x
+
3
y^{''}-3y^'-4y=2sin(x)+4x^2
y
′
′
−
3
y
′
−
4
y
=
2
sin
(
x
)
+
4
x
2
y^{''}+2y^'-3y=3x^2-4x
y
′
′
+
2
y
′
−
3
y
=
3
x
2
−
4
x
y^{''}+9y=18x+36sin(3x)
y
′
′
+
9
y
=
1
8
x
+
3
6
sin
(
3
x
)
y^{''}+2y^'+5y=3sin(x)
y
′
′
+
2
y
′
+
5
y
=
3
sin
(
x
)
y^{''}+2y^'+y=(e^x)/(x^2)
y
′
′
+
2
y
′
+
y
=
e
x
x
2
x^{''}+100x^'+1/(0.0004)x=30
x
′
′
+
1
0
0
x
′
+
1
0
.
0
0
0
4
x
=
3
0
y^{''}-y=1+x^2e^x
y
′
′
−
y
=
1
+
x
2
e
x
y^{''}+9y=cos(3t),y(0)=1,y^'(0)=2
y
′
′
+
9
y
=
cos
(
3
t
)
,
y
(
0
)
=
1
,
y
′
(
0
)
=
2
y^{''}-4y^'-5y=12,5y(0)=0
y
′
′
−
4
y
′
−
5
y
=
1
2
,
5
y
(
0
)
=
0
y^{''}-y^'+y=6sin(x)-3e^{2x}
y
′
′
−
y
′
+
y
=
6
sin
(
x
)
−
3
e
2
x
1/16 (d^2x)/(dt^2)+x=10sin(4t)
1
1
6
d
2
x
dt
2
+
x
=
1
0
sin
(
4
t
)
y^{''}+2y^'+5y=cos(2t)
y
′
′
+
2
y
′
+
5
y
=
cos
(
2
t
)
y^{''}+10y^'+24y=2e^{-4x}(4x-2)
y
′
′
+
1
0
y
′
+
2
4
y
=
2
e
−
4
x
(
4
x
−
2
)
1y^{''}+25y=cos(5x)csc^2(5x)
1
y
′
′
+
2
5
y
=
cos
(
5
x
)
csc
2
(
5
x
)
y^{''}+8y^'+16y=2sin(4t)
y
′
′
+
8
y
′
+
1
6
y
=
2
sin
(
4
t
)
y^{''}+4y=14cos(2x)+21sin(2x)
y
′
′
+
4
y
=
1
4
cos
(
2
x
)
+
2
1
sin
(
2
x
)
y^{''}-y^'=e^xcos(x),y(0)=0,y^'(0)=0
y
′
′
−
y
′
=
e
x
cos
(
x
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
(D^2+5)y=3xe^x
(
D
2
+
5
)
y
=
3
xe
x
y^{''}-2y^'+2y=e^{2t}sin(t)
y
′
′
−
2
y
′
+
2
y
=
e
2
t
sin
(
t
)
y^{''}-6y^'+9y=x^2-x+3
y
′
′
−
6
y
′
+
9
y
=
x
2
−
x
+
3
y^{''}-y=2-x^2
y
′
′
−
y
=
2
−
x
2
y^{''}-2y^'+y=-e^xsin(x)
y
′
′
−
2
y
′
+
y
=
−
e
x
sin
(
x
)
y^{''}-4y=4
y
′
′
−
4
y
=
4
(d^2y)/(dx^2)-2(dy)/(dx)+y=x^2-1
d
2
y
dx
2
−
2
dy
dx
+
y
=
x
2
−
1
y^{''}-4y^'+3y=6
y
′
′
−
4
y
′
+
3
y
=
6
2y^{''}-5y^'-3y=3-x
2
y
′
′
−
5
y
′
−
3
y
=
3
−
x
y^{''}-3y^'+2y=4t+e^{3t}
y
′
′
−
3
y
′
+
2
y
=
4
t
+
e
3
t
2y^{''}-8y^'-4y=-5x^2-12xe^{-x}
2
y
′
′
−
8
y
′
−
4
y
=
−
5
x
2
−
1
2
xe
−
x
y^{''}-5y^'-24y=(t+1)e^t
y
′
′
−
5
y
′
−
2
4
y
=
(
t
+
1
)
e
t
5y^{''}+y^'=-4x,y(0)=0,y^'(0)=-25
5
y
′
′
+
y
′
=
−
4
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
−
2
5
(d^2x)/(dt^2)+(dx)/(dt)=5t
d
2
x
dt
2
+
dx
dt
=
5
t
3y^{''}+2y^'-y=23
3
y
′
′
+
2
y
′
−
y
=
2
3
y^{''}-y^'-6y=45cos(3x)
y
′
′
−
y
′
−
6
y
=
4
5
cos
(
3
x
)
y^{''}+4y^'+3y=8e^{-2x}
y
′
′
+
4
y
′
+
3
y
=
8
e
−
2
x
y^{''}+3y^'+2y=3e^{2t}
y
′
′
+
3
y
′
+
2
y
=
3
e
2
t
y^{''}-8y^'+16y=e^{-x}
y
′
′
−
8
y
′
+
1
6
y
=
e
−
x
y^{'''}-3y^{''}+2y^'=12e^{2x}+24x^2
y
′
′
′
−
3
y
′
′
+
2
y
′
=
1
2
e
2
x
+
2
4
x
2
(d^2y)/(dt^2)-y=e^t,y(0)=1,y^'(0)=1
d
2
y
dt
2
−
y
=
e
t
,
y
(
0
)
=
1
,
y
′
(
0
)
=
1
1
..
2351
2352
2353
2354
2355
..
2459