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ODE First Order ODE Worksheets - Descargar archivos PDF gratuitos

ODE

First Order ODE

Linear

1.\:\:y^{\prime}+y=e^{t}+11

2.\:\:y^{\prime}\cos(x)+y\sin(x)=1

3.\:\:y^{\prime}\cos(x)=y\sin(x)+\sin(2x)

4.\:\:y^{\prime}-2xy=e^{x^{2}}

5.\:\:y^{'}+y=(x+1)^2,\:y(0)=0

6.\:\:2y+(x+1)\frac{dy}{dx}=3x+3,\:y(0)=3

7.\:\:y^{'}-3y=3e^{4t},\:y(0)=5

8.\:\:y^{'}=\frac{1}{3}y-e^{-4x},\:y(0)=7

9.\:\:y^{'}=x+y,\:y(0)=1

10.\:\:x\frac{dy}{dx}+y=x,\:y(1)=1

ODE

First Order ODE

Separable

1.\:\:y^{\prime}=x^{2}y

2.\:\:\frac{dy}{dx}=y^{2}e^{-x}

3.\:\:(x^{2}+9)\frac{dy}{dx}+xy=0

4.\:\:y^{\prime}=y

5.\:\:y^{\prime}+x=xy^{2}

6.\:\:y^{\prime}=y^{2}\cos(x)+4y^{\prime}\sin^{2}(x)

7.\:\:y^{'}(x)=y(x)+2,\:y(0)=0

8.\:\:xyy^{\prime}=1+x^{2}+y^{2}+x^{2}y^{2}

9.\:\:\frac{dy}{dx}=\frac{y^2}{x^3},\:y(1)=1

10.\:\:y^{'}=-4xy^2,\:y(0)=1

ODE

First Order ODE

Bernoulli

1.\:\:y^{\prime}+y=y^{2}(\cos(x)-\sin(x))

2.\:\:x^{3}y^{\prime}=x^{2}y-y^{3}

3.\:\:xy^{\prime}+y^{2}\ln(x)+y=0

4.\:\:x^{2}\frac{dy}{dx}-2xy=3y^{4},\:y(1)=\frac{1}{2}

5.\:\:x^{2}\frac{d}{dx}y+y^{2}=xy

6.\:\:y^{\prime}=y(xy^{3}-1)

7.\:\:\frac{d}{dx}y=y-\frac{1}{2}xy^{2}

8.\:\:xy^{2}y^{\prime}+3x^{3}=y^{3}

9.\:\:xy^{2}\frac{d}{dx}y=x^{2}+y^{3}

10.\:\:xy^{\prime}+y+xy^{2}=0

ODE

First Order ODE

Exact

1.\:\:3y^{2}ty^{\prime}+y^{3}=-2t

2.\:\:\frac{dy}{dx}=\frac{x-y+1}{x+y-3}

3.\:\:2x^{3}yy^{\prime}+3x^{2}y^{2}+7=0

4.\:\: (x^{3}+y^{3})dx+3xy^{2}dy=0

5.\:\:(2x+y+1)dx+(x+2y+3)dy=0

6.\:\:(2x-y)dx+(y-x)dy=0

7.\:\:(x^2-y^2)dx-2xydy=0

8.\:\:x^{2}\sin(x)-\cos(x)y=\sin(x)\frac{dy}{dx}

9.\:\:(x+2y)dx+(2x+3y)dy=0

10.\:\:(3x^{2}+4xy)dx+(2x^{2}+2y)dy=0