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일반적인 미적분학 문제
solvefor y,d(y)=7(2)^y
solvefor
y
,
d
(
y
)
=
7
(
2
)
y
y^{''}+4y^'+5y=1-5x+8(cos(x)-sin(x))
y
′
′
+
4
y
′
+
5
y
=
1
−
5
x
+
8
(
cos
(
x
)
−
sin
(
x
)
)
4x^{''}-4x^'+x= 8/(t^2)e^{t/2}
4
x
′
′
−
4
x
′
+
x
=
8
t
2
e
t
2
-y^{''}+2y^'+3y=1
−
y
′
′
+
2
y
′
+
3
y
=
1
y^{''}-y^'=e^x(3sin(x)+cos(x))
y
′
′
−
y
′
=
e
x
(
3
sin
(
x
)
+
cos
(
x
)
)
4(d^2y)/(dx^2)+9y=15
4
d
2
y
dx
2
+
9
y
=
1
5
y^{''}-y=sin(t),y(0)=0,y^'(0)=0
y
′
′
−
y
=
sin
(
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+5y^'+6y=4x+5
y
′
′
+
5
y
′
+
6
y
=
4
x
+
5
3x^{''}+30x^'+125x=350
3
x
′
′
+
3
0
x
′
+
1
2
5
x
=
3
5
0
y^{''}+y=t^2+1
y
′
′
+
y
=
t
2
+
1
y^{''}+4y^'+4y=5e^{3t}
y
′
′
+
4
y
′
+
4
y
=
5
e
3
t
y^{''}+y^'+5/4 y=3cos(x)
y
′
′
+
y
′
+
5
4
y
=
3
cos
(
x
)
y^{''}+y^'-6y=8+4e^t
y
′
′
+
y
′
−
6
y
=
8
+
4
e
t
u^{''}-3\H(t)=7cos(t),\H(0)=-3/4 ,u^'(0)=0
u
′
′
−
3
H
(
t
)
=
7
cos
(
t
)
,
H
(
0
)
=
−
3
4
,
u
′
(
0
)
=
0
y^{''}+y^'=5x+2e^x
y
′
′
+
y
′
=
5
x
+
2
e
x
y^{''}-8y^'+7y=14
y
′
′
−
8
y
′
+
7
y
=
1
4
y^{''}-y^'-2y=3sin(x)
y
′
′
−
y
′
−
2
y
=
3
sin
(
x
)
y^{''}+5y^'+6y=36t+6
y
′
′
+
5
y
′
+
6
y
=
3
6
t
+
6
y^{''}+y^'=3e^{x/2}
y
′
′
+
y
′
=
3
e
x
2
y^{''}-2y^'-3y=3e^{5t}
y
′
′
−
2
y
′
−
3
y
=
3
e
5
t
y^{''}+36y=8cos(6x)+12sin(6x)
y
′
′
+
3
6
y
=
8
cos
(
6
x
)
+
1
2
sin
(
6
x
)
(d^2y)/(dx^2)+4(dy)/(dx)-5y=24e^x
d
2
y
dx
2
+
4
dy
dx
−
5
y
=
2
4
e
x
(d^2y)/(dx^2)+4(dy)/(dx)+3y=6x^2+19x+5
d
2
y
dx
2
+
4
dy
dx
+
3
y
=
6
x
2
+
1
9
x
+
5
y^{'''}+y^{''}-2y=xe^x+5
y
′
′
′
+
y
′
′
−
2
y
=
xe
x
+
5
(D^4-8D^2+16)y=xe^{2x}
(
D
4
−
8
D
2
+
1
6
)
y
=
xe
2
x
y^{''}+4y^'=sec(2x)
y
′
′
+
4
y
′
=
sec
(
2
x
)
y^{''}+y=2e^{-x},y(0)=0,y^'(0)=0
y
′
′
+
y
=
2
e
−
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+3y^'=e^{-3x}
y
′
′
+
3
y
′
=
e
−
3
x
y^{''}-4y^'+3y=2e^5x
y
′
′
−
4
y
′
+
3
y
=
2
e
5
x
(d^2x)/(dt^2)+5(dx)/(dt)+4x=e^{6t}
d
2
x
dt
2
+
5
dx
dt
+
4
x
=
e
6
t
y^{''}-6y^'+9y=27e^{6x}
y
′
′
−
6
y
′
+
9
y
=
2
7
e
6
x
y^{'''}+4y^{''}+3y^'=2+e^2t
y
′
′
′
+
4
y
′
′
+
3
y
′
=
2
+
e
2
t
y^{''}+y^'-2y=3xe^x
y
′
′
+
y
′
−
2
y
=
3
xe
x
y^{''}+y=3cos(t),y(0)=0,y^'(0)=0
y
′
′
+
y
=
3
cos
(
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+6y^'+5y=e^{-3x}
y
′
′
+
6
y
′
+
5
y
=
e
−
3
x
2y^{''}+3y^'+y=x^3+3sin(x)
2
y
′
′
+
3
y
′
+
y
=
x
3
+
3
sin
(
x
)
(d^2y)/(dx^2)-6(dy)/(dx)+9y=54+18
d
2
y
dx
2
−
6
dy
dx
+
9
y
=
5
4
+
1
8
solvefor d,d(x)=e^{2x^3+4}
solvefor
d
,
d
(
x
)
=
e
2
x
3
+
4
x^{''}+4x=sin(3t)
x
′
′
+
4
x
=
sin
(
3
t
)
(D^2-4D+3)y=9x^2-36x+37
(
D
2
−
4
D
+
3
)
y
=
9
x
2
−
3
6
x
+
3
7
y^{''}+4y=x^2e^{-x},y(0)=0,y^'(0)=1
y
′
′
+
4
y
=
x
2
e
−
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{''}-2y^'-3y=6,y(0)=9,y^'(0)=27
y
′
′
−
2
y
′
−
3
y
=
6
,
y
(
0
)
=
9
,
y
′
(
0
)
=
2
7
y^{''}+y^'-6y=3x+2
y
′
′
+
y
′
−
6
y
=
3
x
+
2
y^{''}-2y^'+2y=2x+2
y
′
′
−
2
y
′
+
2
y
=
2
x
+
2
y^{''}-2y^'-2y=-1+5x^2+x^3
y
′
′
−
2
y
′
−
2
y
=
−
1
+
5
x
2
+
x
3
y^{''}-8y^'+15y=te^{3t}
y
′
′
−
8
y
′
+
1
5
y
=
te
3
t
y^{'''}-3y^{''}+y^'-3y=e^x+2
y
′
′
′
−
3
y
′
′
+
y
′
−
3
y
=
e
x
+
2
y^{''}+k^2y=acos(bx),y(0)=0,y^'(0)=0
y
′
′
+
k
2
y
=
a
cos
(
bx
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}-2y^'+2y=e^x(1/(sin(x)))
y
′
′
−
2
y
′
+
2
y
=
e
x
(
1
sin
(
x
)
)
y^{''}-y^'-6y=5t,y(0)=3,y^'(0)=1
y
′
′
−
y
′
−
6
y
=
5
t
,
y
(
0
)
=
3
,
y
′
(
0
)
=
1
solvefor D,D(x)=x^8-4^4
solvefor
D
,
D
(
x
)
=
x
8
−
4
4
d(x)=120-4x^2
d
(
x
)
=
1
2
0
−
4
x
2
x^{''}+2x^'+3x=t^2+4t
x
′
′
+
2
x
′
+
3
x
=
t
2
+
4
t
y^{''}-2y^'+y=(e^x-1)^2,y(0)=0,y^'(0)=1
y
′
′
−
2
y
′
+
y
=
(
e
x
−
1
)
2
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
(D^2+3D-4)y=15e^x
(
D
2
+
3
D
−
4
)
y
=
1
5
e
x
5y^{''}+y^'=-10x,y(0)=0,y^'(0)=-20
5
y
′
′
+
y
′
=
−
1
0
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
−
2
0
2y^{''}+3y^'+y=gt
2
y
′
′
+
3
y
′
+
y
=
gt
y^{''}-y=2t,y(0)=-2t
y
′
′
−
y
=
2
t
,
y
(
0
)
=
−
2
t
y^{''}=-3y+cos(sqrt(3)x)
y
′
′
=
−
3
y
+
cos
(
√
3
x
)
y^{''}+2y^'+5y=3sin(t)
y
′
′
+
2
y
′
+
5
y
=
3
sin
(
t
)
y^{''}-y^'-6y=62cos(3x)
y
′
′
−
y
′
−
6
y
=
6
2
cos
(
3
x
)
(d^2x)/(dt^2)+k(dx)/(dt)+g=0
d
2
x
dt
2
+
k
dx
dt
+
g
=
0
(d^2y)/(dx^2)+4y=x^2+sin(2x)
d
2
y
dx
2
+
4
y
=
x
2
+
sin
(
2
x
)
y^{''}+8y=2,y(0)=2,y^'(0)=3
y
′
′
+
8
y
=
2
,
y
(
0
)
=
2
,
y
′
(
0
)
=
3
y^{''}+25y=sin(2x)
y
′
′
+
2
5
y
=
sin
(
2
x
)
y^{''}-2y^'+2y=x^2
y
′
′
−
2
y
′
+
2
y
=
x
2
y^{''}-5y^'+7y=2
y
′
′
−
5
y
′
+
7
y
=
2
(d^2y)/(dx^2)-2(dy)/(dx)+2y=3e^xsec(x)
d
2
y
dx
2
−
2
dy
dx
+
2
y
=
3
e
x
sec
(
x
)
y^{''}-25y=6sin(x)
y
′
′
−
2
5
y
=
6
sin
(
x
)
(d^2y)/(dx^2)-2(dy)/(dx)+y=sin(x)
d
2
y
dx
2
−
2
dy
dx
+
y
=
sin
(
x
)
y^{''}+2y^'+6y=e^{-2t},y(0)=2,y^'(0)=1
y
′
′
+
2
y
′
+
6
y
=
e
−
2
t
,
y
(
0
)
=
2
,
y
′
(
0
)
=
1
y^{''}+4y^'+5y=1,y(0)=0,y^'(0)=0
y
′
′
+
4
y
′
+
5
y
=
1
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
10y^{''}+45y^'+2500y=180cos(7pix)
1
0
y
′
′
+
4
5
y
′
+
2
5
0
0
y
=
1
8
0
cos
(
7
π
x
)
y^{''}+4y=sin(t),y(0)=1,y^'(0)=-1
y
′
′
+
4
y
=
sin
(
t
)
,
y
(
0
)
=
1
,
y
′
(
0
)
=
−
1
y^{''}-4y=5e^{2x}+6,y^'(0)=-1,y(0)=0
y
′
′
−
4
y
=
5
e
2
x
+
6
,
y
′
(
0
)
=
−
1
,
y
(
0
)
=
0
y^{'''}+y^{''}-2y=xe^x+15
y
′
′
′
+
y
′
′
−
2
y
=
xe
x
+
1
5
(d^2y)/(dx^2)-(dy)/(dx)+1/4 y=xe^{x/2}
d
2
y
dx
2
−
dy
dx
+
1
4
y
=
xe
x
2
x^{''}+4x=sin(t)
x
′
′
+
4
x
=
sin
(
t
)
3y^{''}-2y^'-y=x^2
3
y
′
′
−
2
y
′
−
y
=
x
2
D(t)=t+5
D
(
t
)
=
t
+
5
y^{''}+2y^'-y=t^{-1}e^t
y
′
′
+
2
y
′
−
y
=
t
−
1
e
t
y^{''}-4y^'-12y=4
y
′
′
−
4
y
′
−
1
2
y
=
4
y^{''}-2y^'+2y=sin(t),y(0)=0,y^'(0)=1
y
′
′
−
2
y
′
+
2
y
=
sin
(
t
)
,
y
(
0
)
=
0
,
y
′
(
0
)
=
1
y^{''}-5y^'+6y=3x^2+5x
y
′
′
−
5
y
′
+
6
y
=
3
x
2
+
5
x
y^{''}+2y^'-3y=5e^{2x},y(0)=0,y^'(0)=a
y
′
′
+
2
y
′
−
3
y
=
5
e
2
x
,
y
(
0
)
=
0
,
y
′
(
0
)
=
a
y^{''}+4y=sin^{22}(x)
y
′
′
+
4
y
=
sin
2
2
(
x
)
y^{''}-3y^'=2-6x
y
′
′
−
3
y
′
=
2
−
6
x
y^{'''}-2y^{''}+y^'=1+xe^x
y
′
′
′
−
2
y
′
′
+
y
′
=
1
+
xe
x
6y^{''}+4y^'-y=25
6
y
′
′
+
4
y
′
−
y
=
2
5
10000x^{''}+1000x^'+22x-60000=0
1
0
0
0
0
x
′
′
+
1
0
0
0
x
′
+
2
2
x
−
6
0
0
0
0
=
0
y^{''}+3y^'+6*x=0
y
′
′
+
3
y
′
+
6
·
x
=
0
y^{''}-8y^'+12y=2x(e^{2x}-e^{-2x})
y
′
′
−
8
y
′
+
1
2
y
=
2
x
(
e
2
x
−
e
−
2
x
)
4q^{''}+8q^'+80q=88t
4
q
′
′
+
8
q
′
+
8
0
q
=
8
8
t
3y^{''}-8y^'-3y=5
3
y
′
′
−
8
y
′
−
3
y
=
5
y^{''}+4y^'-5=2t^2-3t+6
y
′
′
+
4
y
′
−
5
=
2
t
2
−
3
t
+
6
y^{''}+25y=6x,y(0)=1,y^'(0)=5
y
′
′
+
2
5
y
=
6
x
,
y
(
0
)
=
1
,
y
′
(
0
)
=
5
y^{'''}-y^{''}+y^'-y=e^t(t^2+sin(t))
y
′
′
′
−
y
′
′
+
y
′
−
y
=
e
t
(
t
2
+
sin
(
t
)
)
y^{''}+16y=3,y(0)=0,y^'(0)=0
y
′
′
+
1
6
y
=
3
,
y
(
0
)
=
0
,
y
′
(
0
)
=
0
y^{''}+y^'=x,y(0)=1,y^'(0)=0
y
′
′
+
y
′
=
x
,
y
(
0
)
=
1
,
y
′
(
0
)
=
0
y^{''}-12y^'+36y=42x+2
y
′
′
−
1
2
y
′
+
3
6
y
=
4
2
x
+
2
1
..
2360
2361
2362
2363
2364
..
2459