Варианты контрольных заданий Задания для самостоятельной работы.

4y=8x-x², 4y=x+6

y=lnx, 1≤x≤2

x²+y²=9, y≥0, {ох}

(3+e^x)yy^/=e^x

tgxy^/=tgy, y(π/6)=π/4

y=4-x², y=3

y²=x³, 0≤x≤5

y= , x-3y+5=0, {ох}

y(1+lny)+xy^/=0

tgysin²xdx+cos²yctgxdy=0 y(π/4)=π/4

y=-x²-2x, y=0,5x+1

9y²=4x³, 0≤x≤3

x+2y-4=0, y=x, x=0, {оу}

+yy^/ =0

y ^/tgx=-y², y(π/4)=-1

x= , x=0, y=0, y=1

4-y=lnx, 1≤x≤2

2y=x², 8y=x³, {ох}

2xyy^/=1-4x³

xyy^/== , y(1)=π

xy=6, y=7-x

y= , 0≤x≤5

y=x², y=2x, {ох}

4xdx-3ydy=3x²ydy-2xy²dx.

y^/ctgx-y=2, y(π/3)=-1

y=-x²+6x и осью OX

y=0,25x²-0,5lnx, 1≤x≤L

y²=4x, y=2, x=3, {оу}

y^/+xy²+x=0

(1+cosx)xx^/=siny, x(π/4)=2

y=x²+4x, y=x+4

y=lnsinx, π/6≤x≤π/3

y=x²-9, y=-5, {оу}

dx-ydy=x²ydy

cosysinxdy=cosxsinydx, y(π/2)=π/6

x²+y=4x, y=2x

y=0,5x², 0≤x≤

y=x x²+y²=2x, {оу}

(1+x³)y^/-x²y=0

cos²xy^/=y³, y(0)=1/2

y=(x-1)², y²=x-1

y=lnx-2, 1≤x≤2

y=2-x, y=2x-x², {оу}

(yx²+y)y^/=x-xy²=0

cos²(y)x^/=x³, x(0)=1/2

y=3e^x, y=3, x=2

(y-1)²=x³, 0≤x≤5

xy=4, y=1, x=1, {ох}

(e^x+3)dy=y³e^xdx

(1+cosx)y ^/=y²sinx, x(π/2)=-1

y= , x=

9(y+2)²=4x³, 0≤x≤3

xy=6, y=1, x=1, {ох}

y(x+2)y ^/=y²+4

(2+y)y ^/= , x(0)=π/2

y²+x-5=0, x=0

x²+(y-1)²=4, 0≤x≤1

y=x²+1, y=3x+1, {ох}

y ^/=

y ^/=4x³cos²y, y(0)=π/4

x=4-(y-1)², x=0

y-2= x²- lnx, 1≤x≤e

y²=4-x, x=1, {оу}

xyy^/=2+y²

tgyx^/=tgx, y(π/6)=π/4

x=4y²-4y+3, x=0

y+2=lnsinx, π/6≤x≤π/3

y=2x-x², y=x, {оу}

(x²+x²y³)dy=(y²+y²x³)dy

dx= , y(π)=2

x=7e^x, x=3, y=7

y-3=lncosx, 0≤x≤π/3

y+x-5=0, yx=4, {ох}

e^x(1+e^x)dx+e^y(1+e^x)dy=0

y²cos²xy^/=1/3 y(0)=0

y=32-x ², 4x+y=0

2y-1=x², 0≤x≤

y=8-x², y=x², {ох}

y^/=

x²cos²yx^/=1/3, x(0)=0

y=-x²+6x, y=x+4

x²+y²=4, 0≤x≤1

y=3x-x², y=2

2xdx-2ydy=x²ydy-2xy²dx

y ^/tgx+x=1, y(0)=0

4y=x², 4x=y²

(4-y)²=x³, 0≤x≤5

y²=5x, 5y=x², {ох}

y^/=

y^/=y²ctgx, y(π/2)=-1

y=x+4, y²=1+x

(y-1)²=9x³, 0≤x≤3

xy=2, x+2y-5=0, {ох}

=

yy^/=- , y(0)=π/2

x=1, y²=4-x

x²+(y-5)²=4, 0≤x≤1

y=x²/2, y=x³/8, {ох}

xydy=(2+x²)dx

y^/=- , y(-π/2)=e

xy=4, x+y-5=0

2+4y=x²-2lnx, 0≤x≤e

y²=3x, x²=3y, {ох}

x dx+y dy=0

(2+cosx)y^/=ysinx, y(π)=e

y=8-x², y=x²

7+y=lnsinx, π/3≤x≤ π/2

y=e^2x, y=1, x=1, {ох}

(x²-1)y^/=2y²

y^/tgx-y=2, y(π/4)=-1

.

xy=2, x+2y-6=0

y=3+lncosx, π/6≤x≤π/3

y=x²-2x+3, y=0, x=1, x=2, {ох}

x²y^/-(2x-1)y=0

y^/=tgxtgy, y(0)=π/6

.

y²=3x, x² =3y

2y-7=x², 0≤x≤

x²+4y-16=0, x-2y+4=0, {ох}

y^/+ y=0

y^/tgx-y=1, y(π/3)=0

.

y=x²-5x+6 y=0, x=-1, x=2

y-3=lnx, 1≤x≤2

y=e^x, y=e^-x, x=-1, {ох}

yy^/=

cosxsinydy=sinxcosydx, y(0)=π/4

y=e^x, y=e^-x, x=-1

(y-4)²=x³, 0≤x≤5

y=x², y=2-x⁴, {ох}

y^/+ =0

y³y^/=1+2x, y(0)=2

x²+y-16=0 y=x

(y-1)²=25x³, 0≤x≤3

y=2x², y=3-x⁴, {ох}

xx^/+y=1

(1+cosx)yy^/=sinx, y(π/4)=2

y=x²+6x, y=5-x⁴

(y+5)²+ x²=4, 1≤x≤1

2y=3 , 4y=4-x, {ох}

xydy+(x+1)dx=0

y^/tgx+y=2, y(π/4)=1

y=x²+4, y=2x+1

4y+1=x²-2lnx, 1≤x≤e

y²=2x-2, y=x-1, {оу}

y(x²+1)y^/=1+y²

(1+e^x)yy^/=e^x, y(0)=1

y²-2x+2=0, x-y-1=0

y-2/3=lnsinx, π/3≤x≤ π/2

2y=3 , 4y=4-x², {ох}

xyy^/=1-x²

y^/ctgx+y=0, y(π/3)=1

y=4x-x⁴, y=2x

y+1/2=lncosx, 0≤x≤ π/3

y=2^x, y=0, x=1, x=3, {ох}

tgxsin²ydx=cos²xctgydy

(x²-1)y^/+2xy²=0, y( )=1

.

y=3x, x=y, x=2

3+2y-3= x², 0≤x≤

y²=4x, y=x, {оу}

y^/=tgxtgy

x²y²y^/=1-x² y(1)=0