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First Order ODE Bernoulli Worksheets - 下载免费 PDF

ODE

First Order ODE

Bernoulli

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Answers

ODE

First Order ODE

Bernoulli

1. y=\frac{1}{-\sin(x)+c_{1}e^{x}}

2. y=\frac{x}{\sqrt{2\ln(x)+c_{1}}},y=-\frac{x}{\sqrt{2\ln(x)+c_{1}}}

3. y=\frac{1}{-\ln(x)-1+c_{1}x}

4. y=\frac{\sqrt[3]{5}x^{2}}{\sqrt[3]{-9x^{5}+49}}

5. y=\frac{x}{\ln(x)+c_{1}}

6. y=\sqrt[3]{\frac{3}{3x+1+3c_{1}e^{3x}}}

7. y=\frac{2e^{x}}{e^{x}x-e^{x}+c_{1}}

8. y=x\sqrt[3]{-9\ln(x)+c_{1}}

9. y=-\sqrt[3]{x^{2}}\sqrt[3]{3-c_{1}x}

10. y=\frac{1}{x(\ln(x)+c_{1})}