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일반적인 미적분학 문제
2y^{''}+27y=e^t-e^{-t},y(0)=0,y^'(0)=2
2
y
′
′
+
2
7
y
=
e
t
−
e
−
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
2
y^{''}-y^'+2y=6e^{1/2}
y
′
′
−
y
′
+
2
y
=
6
e
1
2
y^{''}+16y=2csc^2(4x)
y
′
′
+
1
6
y
=
2
csc
2
(
4
x
)
y^{''}+5y^'+6y=sin(x)-cos(2x)
y
′
′
+
5
y
′
+
6
y
=
sin
(
x
)
−
cos
(
2
x
)
y^{''}-10y^'+25=e^{5x}ln(4+x^2)
y
′
′
−
1
0
y
′
+
2
5
=
e
5
x
ln
(
4
+
x
2
)
y^{''}+y=4x^2
y
′
′
+
y
=
4
x
2
y^{''}+4y+3y=9e^{-3x}
y
′
′
+
4
y
+
3
y
=
9
e
−
3
x
y^{'''}+4y^'=sec(x)cos(x)
y
′
′
′
+
4
y
′
=
sec
(
x
)
cos
(
x
)
y^{''}+3y^'+2y=6e^t,y(0)=1,y^'(0)=2
y
′
′
+
3
y
′
+
2
y
=
6
e
t
,
y
(
0
)
=
1
,
y
′
(
0
)
=
2
y^{''}+6y^'+9y=5+5x
y
′
′
+
6
y
′
+
9
y
=
5
+
5
x
y^{'''}+y^{''}+y^'+y=e^{-t}+15t
y
′
′
′
+
y
′
′
+
y
′
+
y
=
e
−
t
+
1
5
t
y^{''}+9y=e^x
y
′
′
+
9
y
=
e
x
y^{''''}+8y^{''}+16y=48+cos(4t)
y
′
′
′
′
+
8
y
′
′
+
1
6
y
=
4
8
+
cos
(
4
t
)
y^{''}+16y=32t
y
′
′
+
1
6
y
=
3
2
t
y^{''}+4y^'+6y=4e^{-2x}cos(x)
y
′
′
+
4
y
′
+
6
y
=
4
e
−
2
x
cos
(
x
)
y^{''}+2y^'+5y=24e^{-t}cos(2t)
y
′
′
+
2
y
′
+
5
y
=
2
4
e
−
t
cos
(
2
t
)
y^{''}-5y^'+4y= 6/(1+e^{-2x)}
y
′
′
−
5
y
′
+
4
y
=
6
1
+
e
−
2
x
y^{''}+y=c
y
′
′
+
y
=
c
(d^2y)/(dx^2)-6(dy)/(dx)+8y=8e^{4x}
d
2
y
dx
2
−
6
dy
dx
+
8
y
=
8
e
4
x
(d^2y)/(dx^2)+2(dy)/(dx)=x
d
2
y
dx
2
+
2
dy
dx
=
x
y^{''}+16y=3csc^2(4x)
y
′
′
+
1
6
y
=
3
csc
2
(
4
x
)
y^{''}-4y^'+3y=(x^2-3x)e^{-x}
y
′
′
−
4
y
′
+
3
y
=
(
x
2
−
3
x
)
e
−
x
y^{''}+y=5
y
′
′
+
y
=
5
y^{''}+y=8
y
′
′
+
y
=
8
y^{''}+2y^'+3y=6x+1
y
′
′
+
2
y
′
+
3
y
=
6
x
+
1
y^{''}+2y=4^3+5x^2-x+7
y
′
′
+
2
y
=
4
3
+
5
x
2
−
x
+
7
y^{''}+4y^'+6y=1+e^{-x},y(0)=0,y^'(0)=0
y
′
′
+
4
y
′
+
6
y
=
1
+
e
−
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}-2/5 y^'-2/25 y=4e^t
y
′
′
−
2
5
y
′
−
2
2
5
y
=
4
e
t
y^{''}+2y=x+1,y(0)=1,y^'(0)=0
y
′
′
+
2
y
=
x
+
1
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
y^{''}-4y^'+4y=t,y(0)=0,y^'(0)=1
y
′
′
−
4
y
′
+
4
y
=
t
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{''}+y^'=cos(2x)
y
′
′
+
y
′
=
cos
(
2
x
)
y^{''}-y^'=4x+3
y
′
′
−
y
′
=
4
x
+
3
y^{''}-3y^'+2y=x,y^1(0)=e^x
y
′
′
−
3
y
′
+
2
y
=
x
,
y
1
(
0
)
=
e
x
y^{''}-4/9 y=x^3-2
y
′
′
−
4
9
y
=
x
3
−
2
x^{''}-4x^'+4x=84t^2e^{2t}
x
′
′
−
4
x
′
+
4
x
=
8
4
t
2
e
2
t
y^{''}+25y=25,y(0)=1,y^'(0)=5
y
′
′
+
2
5
y
=
2
5
,
y
(
0
)
=
1
,
y
′
(
0
)
=
5
y^{''}-2y^'-3y=e^{4x}
y
′
′
−
2
y
′
−
3
y
=
e
4
x
y^{''}+10y^'+25y=-8-5x+25x^2
y
′
′
+
1
0
y
′
+
2
5
y
=
−
8
−
5
x
+
2
5
x
2
10x^{''}+200x=600sin(125t)
1
0
x
′
′
+
2
0
0
x
=
6
0
0
sin
(
1
2
5
t
)
5y^{''}+6y^'+y=x^3+18x^2+32x+13
5
y
′
′
+
6
y
′
+
y
=
x
3
+
1
8
x
2
+
3
2
x
+
1
3
y^{''}-6y^'+8y=3+e^{-2t}
y
′
′
−
6
y
′
+
8
y
=
3
+
e
−
2
t
(d^2y)/(dx^2)-y=cosh(x)+x
d
2
y
dx
2
−
y
=
cosh
(
x
)
+
x
y^{''}-y^'=e^{2x}
y
′
′
−
y
′
=
e
2
x
y^{''''}+8y^{''}+16y=64+cos(4t)
y
′
′
′
′
+
8
y
′
′
+
1
6
y
=
6
4
+
cos
(
4
t
)
(d^2x)/(dt^2)+25x=30cos(6t)
d
2
x
dt
2
+
2
5
x
=
3
0
cos
(
6
t
)
y^{''}-6y^'+5y=3x+e^x,y(0)=0,y^'(0)=2
y
′
′
−
6
y
′
+
5
y
=
3
x
+
e
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
2
y^{''}-y^'-2y=2e^{3x}
y
′
′
−
y
′
−
2
y
=
2
e
3
x
y^{''}+2y^'+y=9-e^{2x},y(0)=0,y^'(0)=1
y
′
′
+
2
y
′
+
y
=
9
−
e
2
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
(3d^2+3)y=3x
(
3
d
2
+
3
)
y
=
3
x
y^{''}+5y^'+6y=4+5x
y
′
′
+
5
y
′
+
6
y
=
4
+
5
x
y^{''}+3y^'-10y=20+5e^{3x}
y
′
′
+
3
y
′
−
1
0
y
=
2
0
+
5
e
3
x
x^{''}+4x^'+14x=9cos(3t)
x
′
′
+
4
x
′
+
1
4
x
=
9
cos
(
3
t
)
y^{''}+6y^'+9y=4sin(6t)
y
′
′
+
6
y
′
+
9
y
=
4
sin
(
6
t
)
y^{''}+9y=t+3,y(0)=1,y^'(0)=2
y
′
′
+
9
y
=
t
+
3
,
y
(
0
)
=
1
,
y
′
(
0
)
=
2
y^{''}-5y^'+2y=6t^2+2t+7
y
′
′
−
5
y
′
+
2
y
=
6
t
2
+
2
t
+
7
y^{''}+5y^'+80y=220cos(11t)
y
′
′
+
5
y
′
+
8
0
y
=
2
2
0
cos
(
1
1
t
)
y^{''}-y=-1
y
′
′
−
y
=
−
1
y^{''}+10y^'+16=10
y
′
′
+
1
0
y
′
+
1
6
=
1
0
y^{''}+y-cos(2x)=0
y
′
′
+
y
−
cos
(
2
x
)
=
0
y^{'''}-2y^{''}+10y^'=250e^{5x}
y
′
′
′
−
2
y
′
′
+
1
0
y
′
=
2
5
0
e
5
x
y^{'''}-y^{''}-4y^'+4=0
y
′
′
′
−
y
′
′
−
4
y
′
+
4
=
0
y^{''}-9y=4e^{-5t}
y
′
′
−
9
y
=
4
e
−
5
t
y^{''}+4y=3cos(at)
y
′
′
+
4
y
=
3
cos
(
at
)
y^{'''}+9y^{''}+27y^'+27y=7e^{-3x}
y
′
′
′
+
9
y
′
′
+
2
7
y
′
+
2
7
y
=
7
e
−
3
x
(d^2y)/(dx^2)-6(dy)/(dx)=2x^2-x+1
d
2
y
dx
2
−
6
dy
dx
=
2
x
2
−
x
+
1
y^{''}-3y-5=e^2-3cos(3x)
y
′
′
−
3
y
−
5
=
e
2
−
3
cos
(
3
x
)
y^{''}+36y=24sin(6x)
y
′
′
+
3
6
y
=
2
4
sin
(
6
x
)
y^{''}+6y=g(t)
y
′
′
+
6
y
=
g
(
t
)
y^{''''}-4y^{'''}+6y^{''}-4y^'+y=e^x
y
′
′
′
′
−
4
y
′
′
′
+
6
y
′
′
−
4
y
′
+
y
=
e
x
2x^{''}+5x^'+2x=2e-2t-t
2
x
′
′
+
5
x
′
+
2
x
=
2
e
−
2
t
−
t
y^{''}+5y^'+6y=te^t
y
′
′
+
5
y
′
+
6
y
=
te
t
x^{''}+2^2*x=3*cos(bt)
x
′
′
+
2
2
·
x
=
3
·
cos
(
bt
)
y^{''}+36y=36sin(6t)
y
′
′
+
3
6
y
=
3
6
sin
(
6
t
)
y^{''}+y=9x^2
y
′
′
+
y
=
9
x
2
y^{''}-5y^'+4y=-3t^2
y
′
′
−
5
y
′
+
4
y
=
−
3
t
2
y^{''}-5y^'=x^2-2x
y
′
′
−
5
y
′
=
x
2
−
2
x
y^{''}-2y^'+y=cos(2x)
y
′
′
−
2
y
′
+
y
=
cos
(
2
x
)
y^{''}=y+e^{2x}e^{e^x}
y
′
′
=
y
+
e
2
x
e
e
x
y^{''}+4y^'=t^2+2e^t
y
′
′
+
4
y
′
=
t
2
+
2
e
t
y^'+y^{''}+y=xe^x
y
′
+
y
′
′
+
y
=
xe
x
y^{''}+2y^'-15y=(2x+1)e^{3x}+10
y
′
′
+
2
y
′
−
1
5
y
=
(
2
x
+
1
)
e
3
x
+
1
0
y^{''}-y^'-2y=2t^2-5
y
′
′
−
y
′
−
2
y
=
2
t
2
−
5
y^{''}-3y^'-4y=2^{t-2},y(2)=1,y^'(2)=-1
y
′
′
−
3
y
′
−
4
y
=
2
t
−
2
,
y
(
2
)
=
1
,
y
′
(
2
)
=
−
1
y^{''}+4y=cos(2)(x)
y
′
′
+
4
y
=
cos
(
2
)
(
x
)
(d^2-2d+2)y=(x+e^x)sin(x)
(
d
2
−
2
d
+
2
)
y
=
(
x
+
e
x
)
sin
(
x
)
y^{''}-y=(2e^{2x})/(e^{2x)+1}
y
′
′
−
y
=
2
e
2
x
e
2
x
+
1
(d^2y)/(dx^2)-2(dy)/(dx)+y=4sin(x)
d
2
y
dx
2
−
2
dy
dx
+
y
=
4
sin
(
x
)
y^{''}-4y^'+3y=e^x
y
′
′
−
4
y
′
+
3
y
=
e
x
y^{''}+4y^'+5y= 1/x e^{2x}sin(x)
y
′
′
+
4
y
′
+
5
y
=
1
x
e
2
x
sin
(
x
)
y^{''}+4y=-16e^{-2x}+2sin(x)
y
′
′
+
4
y
=
−
1
6
e
−
2
x
+
2
sin
(
x
)
y^{''}+4y^'=8x+1
y
′
′
+
4
y
′
=
8
x
+
1
y^{''}-y=2(e^xe^{-x})^{-1}
y
′
′
−
y
=
2
(
e
x
e
−
x
)
−
1
4y^{''}-y=xe^{1/2 x}
4
y
′
′
−
y
=
xe
1
2
x
y^{''}+2y^'+y=3cos(t)
y
′
′
+
2
y
′
+
y
=
3
cos
(
t
)
y^{''}+3y^'+2y=cos(x)-sin(2x)
y
′
′
+
3
y
′
+
2
y
=
cos
(
x
)
−
sin
(
2
x
)
x^{''}+4x^'+5x=e^{-2}tsin(t)
x
′
′
+
4
x
′
+
5
x
=
e
−
2
t
sin
(
t
)
solvefor d,d(t)=-16t^2+32t+40
solvefor
d
,
d
(
t
)
=
−
1
6
t
2
+
3
2
t
+
4
0
x^{''}+81x=sin(7t)
x
′
′
+
8
1
x
=
sin
(
7
t
)
y^{''}+2y^'=te^{-t}
y
′
′
+
2
y
′
=
te
−
t
y^{''}+4y^'+5y=2cos(x)-2sin(x)
y
′
′
+
4
y
′
+
5
y
=
2
cos
(
x
)
−
2
sin
(
x
)
1
..
2357
2358
2359
2360
2361
..
2459