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일반적인 미적분학 문제
y^{''}+4y=t^2+8e^t,y(0)=0,y^'(0)=1
y
′
′
+
4
y
=
t
2
+
8
e
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{'''}+49y^'=tan(7x)
y
′
′
′
+
4
9
y
′
=
tan
(
7
x
)
y^{''}+ay^'=e^{3t}
y
′
′
+
ay
′
=
e
3
t
4y^{''}-11y^'-3y=5e^{3x}
4
y
′
′
−
1
1
y
′
−
3
y
=
5
e
3
x
선의 y^{''}-3y^'+2y=e^x
linear
y
′
′
−
3
y
′
+
2
y
=
e
x
y^{''}-y^'+y=(2e^{3t}+5t)^7
y
′
′
−
y
′
+
y
=
(
2
e
3
t
+
5
t
)
7
(d^2y)/(dx^2)-9(dy)/(dx)+5y=xe^x
d
2
y
dx
2
−
9
dy
dx
+
5
y
=
xe
x
y^{''}+4y^'+4y=e^{-t},y(0)=0,y^'(0)=1
y
′
′
+
4
y
′
+
4
y
=
e
−
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{''}-2y^'-3y=3t^2+4t-5
y
′
′
−
2
y
′
−
3
y
=
3
t
2
+
4
t
−
5
y^{''}-y=7.1cos(t),y(0)=0,y^'(0)=7.1
y
′
′
−
y
=
7
.
1
cos
(
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
7
.
1
y^{''}-4y^'+3y=8e^x
y
′
′
−
4
y
′
+
3
y
=
8
e
x
y^{''}+3y=t^3,y(0)=0,y^'(0)=0
y
′
′
+
3
y
=
t
3
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{'''}+2y^'-y^'-2y=sin(3t)
y
′
′
′
+
2
y
′
−
y
′
−
2
y
=
sin
(
3
t
)
(D^2+1)y=sec^2(x)
(
D
2
+
1
)
y
=
sec
2
(
x
)
y^{''}+2y^'+y=e^{-t}sqrt(1+t)
y
′
′
+
2
y
′
+
y
=
e
−
t
√
1
+
t
y^{''}-4y^'+4y=cos(2x)
y
′
′
−
4
y
′
+
4
y
=
cos
(
2
x
)
2y^{''}-y^'-3y=3xe^{2x}
2
y
′
′
−
y
′
−
3
y
=
3
xe
2
x
y^{''}+y=x^2+1,y(0)=3,y(1)=0
y
′
′
+
y
=
x
2
+
1
,
y
(
0
)
=
3
,
y
(
1
)
=
0
D(D+3)y=x(5+e^x)
D
(
D
+
3
)
y
=
x
(
5
+
e
x
)
y^{''}+2y^'-3y=4e^{2t}
y
′
′
+
2
y
′
−
3
y
=
4
e
2
t
y^{''}-y=e^tcos(t),y(0)=0,y^'(0)=0
y
′
′
−
y
=
e
t
cos
(
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+y=1,y(0)=2,y^'(0)=1
y
′
′
+
y
=
1
,
y
(
0
)
=
2
,
y
′
(
0
)
=
1
y^{''}-2y^'+y=t^{-4}e^t
y
′
′
−
2
y
′
+
y
=
t
−
4
e
t
y^{''}+y^'=10x^4+2
y
′
′
+
y
′
=
1
0
x
4
+
2
y^{''}-2y^'-3y=x-e^x
y
′
′
−
2
y
′
−
3
y
=
x
−
e
x
x^{''}-4x=3t
x
′
′
−
4
x
=
3
t
(d^2y)/(dx^2)-6y=e^{3x}(x^2+2)
d
2
y
dx
2
−
6
y
=
e
3
x
(
x
2
+
2
)
2y^{''}+y^'+2y=1,y(0)=0,y^'(0)=0
2
y
′
′
+
y
′
+
2
y
=
1
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+y=(sec(x))^2
y
′
′
+
y
=
(
sec
(
x
)
)
2
(d^2y)/(dx^2)+2(dy)/(dx)+y=4sinh(x)
d
2
y
dx
2
+
2
dy
dx
+
y
=
4
sinh
(
x
)
2q^{''}+10q^'+12q=e^{-3t}
2
q
′
′
+
1
0
q
′
+
1
2
q
=
e
−
3
t
(d^2y)/(dx^2)+12(dy)/(dx)+32y=160
d
2
y
dx
2
+
1
2
dy
dx
+
3
2
y
=
1
6
0
y^{''}-4y^'=16t+36,y(-2)=2,y^'(-2)=-1
y
′
′
−
4
y
′
=
1
6
t
+
3
6
,
y
(
−
2
)
=
2
,
y
′
(
−
2
)
=
−
1
(d^2y)/(dx^2)+a(dy)/(dx)=b
d
2
y
dx
2
+
a
dy
dx
=
b
y^{''''}-5y^{''}+4y=20e^{3x}
y
′
′
′
′
−
5
y
′
′
+
4
y
=
2
0
e
3
x
y^{''}+36y=12tan(6t)
y
′
′
+
3
6
y
=
1
2
tan
(
6
t
)
(-8x^{''}-16x^'+24)=8e^{2t}
(
−
8
x
′
′
−
1
6
x
′
+
2
4
)
=
8
e
2
t
y^{''}-y^'+2y=4e^x
y
′
′
−
y
′
+
2
y
=
4
e
x
y^{''}-3y^'-6y=2e^{2x}+4
y
′
′
−
3
y
′
−
6
y
=
2
e
2
x
+
4
(4d^4+20d^3+35d^2+25d+6)y=o
(
4
d
4
+
2
0
d
3
+
3
5
d
2
+
2
5
d
+
6
)
y
=
o
2y^{''}+4y^'+8y=10cos(2t)
2
y
′
′
+
4
y
′
+
8
y
=
1
0
cos
(
2
t
)
y^{''}-7y^'+12y=e^x
y
′
′
−
7
y
′
+
1
2
y
=
e
x
(d^2y)/(dx^2)-2(dy)/(dx)+y=1+3x+x^2
d
2
y
dx
2
−
2
dy
dx
+
y
=
1
+
3
x
+
x
2
y^{''}-3y^'-4y=5cos(x)+1389e^{-2x}
y
′
′
−
3
y
′
−
4
y
=
5
cos
(
x
)
+
1
3
8
9
e
−
2
x
x^{''}-18x^'+81x=3te^{9t}
x
′
′
−
1
8
x
′
+
8
1
x
=
3
te
9
t
y^{''}+2y^'+y=2x^2+4x+2
y
′
′
+
2
y
′
+
y
=
2
x
2
+
4
x
+
2
y^{'''}+3y^{''}+3y^'+y=e-x
y
′
′
′
+
3
y
′
′
+
3
y
′
+
y
=
e
−
x
y^{''}-8y^'+16y=t^{-5}e^{4t}
y
′
′
−
8
y
′
+
1
6
y
=
t
−
5
e
4
t
x^{''}+7x^'+12x=e^{2t}+cos(4t)
x
′
′
+
7
x
′
+
1
2
x
=
e
2
t
+
cos
(
4
t
)
y^{''}+2y^'+2y=cos(x)
y
′
′
+
2
y
′
+
2
y
=
cos
(
x
)
y^{'''}-y^{''}-16y^'+16y=8-e^x+e^{4x}
y
′
′
′
−
y
′
′
−
1
6
y
′
+
1
6
y
=
8
−
e
x
+
e
4
x
y^{''}-2y^'+y=-4e^x+3x^2
y
′
′
−
2
y
′
+
y
=
−
4
e
x
+
3
x
2
y^{''}+3y^'+4y=8x+2
y
′
′
+
3
y
′
+
4
y
=
8
x
+
2
(d^2+d)y=x^2+2x-3
(
d
2
+
d
)
y
=
x
2
+
2
x
−
3
2y^{''}+12y=6tan(3x)
2
y
′
′
+
1
2
y
=
6
tan
(
3
x
)
y^{''}+4y^'+5y=-5x+3e^{(-x)}
y
′
′
+
4
y
′
+
5
y
=
−
5
x
+
3
e
(
−
x
)
(d^2-4d+4)y=5sin^3(x)
(
d
2
−
4
d
+
4
)
y
=
5
sin
3
(
x
)
y^{''}-9y=(x^2-2)sin(3x)
y
′
′
−
9
y
=
(
x
2
−
2
)
sin
(
3
x
)
y^{''}-3y^'+2y=11e^3x,y^1(0)=ex
y
′
′
−
3
y
′
+
2
y
=
1
1
e
3
x
,
y
1
(
0
)
=
ex
y^{''}+4y=8x^2+7x
y
′
′
+
4
y
=
8
x
2
+
7
x
y^{''}-4y^'=x
y
′
′
−
4
y
′
=
x
10y^{''}+90y^'+1/(0.005)y=500sin(x)
1
0
y
′
′
+
9
0
y
′
+
1
0
.
0
0
5
y
=
5
0
0
sin
(
x
)
y^{''}+3y=cos(sqrt(3)x)
y
′
′
+
3
y
=
cos
(
√
3
x
)
y^{''}+3y^'=9
y
′
′
+
3
y
′
=
9
y^{''}-4y^'=e^{4x}
y
′
′
−
4
y
′
=
e
4
x
y^{''}-11y^'+24y=280e^t
y
′
′
−
1
1
y
′
+
2
4
y
=
2
8
0
e
t
y^{''}+9y=5sec(3x)
y
′
′
+
9
y
=
5
sec
(
3
x
)
y^{''}-3y^'+2y=(e^{3x})/(e^{2x)+1}
y
′
′
−
3
y
′
+
2
y
=
e
3
x
e
2
x
+
1
y^{''}+10000y=100sin(50x)
y
′
′
+
1
0
0
0
0
y
=
1
0
0
sin
(
5
0
x
)
y^{''}+10y^'+15=0
y
′
′
+
1
0
y
′
+
1
5
=
0
(d^2x)/(dt^2)+(dx)/(dt)+x=1
d
2
x
dt
2
+
dx
dt
+
x
=
1
y^{''}+y^'-y=t*e^t
y
′
′
+
y
′
−
y
=
t
·
e
t
x^{''}+12x^'+11x=9cos(2t)
x
′
′
+
1
2
x
′
+
1
1
x
=
9
cos
(
2
t
)
y^{''}-4y^'+3y=3e^{2x}
y
′
′
−
4
y
′
+
3
y
=
3
e
2
x
y^{''}-7y^'=5x*e^x
y
′
′
−
7
y
′
=
5
x
·
e
x
y^{''}+y^'-32y=16cos(x)
y
′
′
+
y
′
−
3
2
y
=
1
6
cos
(
x
)
y^{''}+4y=32sin(4t),y(0)=1
y
′
′
+
4
y
=
3
2
sin
(
4
t
)
,
y
(
0
)
=
1
y^{''}+y^'-2y=4e^{3t}
y
′
′
+
y
′
−
2
y
=
4
e
3
t
y^{''}-12y^'+5y=-8sin(t)
y
′
′
−
1
2
y
′
+
5
y
=
−
8
sin
(
t
)
4y^{''}+y=t-cos(t/2)
4
y
′
′
+
y
=
t
−
cos
(
t
2
)
y^{''}+4y=2e^{2t},y(0)=1,y^'(0)=0
y
′
′
+
4
y
=
2
e
2
t
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
y^{''}-y^'-6y=2sin(t)
y
′
′
−
y
′
−
6
y
=
2
sin
(
t
)
D(x)=105.6-2.4x
D
(
x
)
=
1
0
5
.
6
−
2
.
4
x
x^{''}+4x^'+43x=10cos(6t)
x
′
′
+
4
x
′
+
4
3
x
=
1
0
cos
(
6
t
)
y^{''}-3y^{''}+3y^'-y=x-2e^x
y
′
′
−
3
y
′
′
+
3
y
′
−
y
=
x
−
2
e
x
y^{''}+4y^'+5y=1-5x+8cos(x)-8sin(x)
y
′
′
+
4
y
′
+
5
y
=
1
−
5
x
+
8
cos
(
x
)
−
8
sin
(
x
)
y^{''}+16y=4e^{2t}+4sin(2t)
y
′
′
+
1
6
y
=
4
e
2
t
+
4
sin
(
2
t
)
x^{''}+x=acos(t)
x
′
′
+
x
=
a
cos
(
t
)
y^{''}+36y=36sec^2(6x)
y
′
′
+
3
6
y
=
3
6
sec
2
(
6
x
)
y^{'''}+25y^'=10sin(5t)-4t^2
y
′
′
′
+
2
5
y
′
=
1
0
sin
(
5
t
)
−
4
t
2
y^{''}+y=1,y(0)=0,y^'(0)=1
y
′
′
+
y
=
1
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{''}+2y^'+y=4000sec(40x)
y
′
′
+
2
y
′
+
y
=
4
0
0
0
sec
(
4
0
x
)
ax^{''}+bx^'+c=0
ax
′
′
+
bx
′
+
c
=
0
(d^2y)/(dt^2)-3(dy)/(dt)-10y=4e^{5t}
d
2
y
dt
2
−
3
dy
dt
−
1
0
y
=
4
e
5
t
y^{''}-y^'-12y=e^2x+e^x-2
y
′
′
−
y
′
−
1
2
y
=
e
2
x
+
e
x
−
2
y^{''}+6y^'+5y=36e^x,y(0)=-2,y^'(0)=4
y
′
′
+
6
y
′
+
5
y
=
3
6
e
x
,
y
(
0
)
=
−
2
,
y
′
(
0
)
=
4
y^{''}+y^'-12y=(e^x)/x
y
′
′
+
y
′
−
1
2
y
=
e
x
x
(6D^2+4D+2)y=xe^{-2x}
(
6
D
2
+
4
D
+
2
)
y
=
xe
−
2
x
-21y+4y^'+y^{''}=t+1
−
2
1
y
+
4
y
′
+
y
′
′
=
t
+
1
y^{''}+14y^'+50y=6e^{-7t}cos(t)
y
′
′
+
1
4
y
′
+
5
0
y
=
6
e
−
7
t
cos
(
t
)
1
..
2359
2360
2361
2362
2363
..
2459