Dr.Harswaroop Sharma Mathematics Solution Class 12 Chapter 9 अवकल समीकरण (Differential Equation) Exercise 9F

  

    

प्रश्नावली - 9F

निम्नलिखित अवकल समीकरणों को हल कीजिए:

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Question 1

1. $2 x^2 d y=\left(x^2+y^2\right) d x$

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Question 2

2. $\left(x y-x^2\right) d y=y^2 d x$

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Question 3

3. $y^2+x^2 \frac{d y}{d x}=x y \frac{d y}{d x}$

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Question 4

4. $\frac{d y}{d x}=\frac{x^2-y^2}{x y}$

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Question 5

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

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Question 6

6. $\left(x^2+3 x y+y^2\right) d x-x^2 d y=0$

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Question 7

7. $(x-y) d y-(x+y) d x=0$

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Question 8

8. $\frac{d y}{d x}=\frac{x+y}{x}$

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Question 9

9. $\left(x^3+y^3\right) d y-x^2 y d x=0$

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Question 10

10. $y^2 d x+\left(x^2-x y+y^2\right) d y=0$

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Question 11

11. $x^2 \frac{d y}{d x}=x^2-2 y^2+x y$

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Question 12

12. $\left(x^2+x y\right) d y=\left(x^2+y^2\right) d x$

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Question 13

13. $x \frac{d y}{d x}=x+y$

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Question 14

14. $x \frac{d y}{d x}-y+x \sin \left(\frac{y}{x}\right)=0$

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Question 15

15. $x d y-y d x=\sqrt{x^2+y^2} d x$

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Question 16

16. $\left(x^2-y^2\right) d x+2 x y d y=0$

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Question 17

17. $x \cos \frac{y}{x}(y d x+x d y)=y \sin \frac{y}{x}(x d y-y d x)$.

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Question 18

18. $\left\{x \cos \left(\frac{y}{x}\right)+y \sin \left(\frac{y}{x}\right)\right\} y d x=\left\{y \sin \left(\frac{y}{x}\right)-x \cos \left(\frac{y}{x}\right)\right\} x d y$

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Question 19

19. $y d x+x \log \left(\frac{y}{x}\right) d y-2 x d y=0$

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Question 20

20. $\left(1+e^{x / y}\right) d x+e^{\frac{x}{y}}\left(1-\frac{x}{y}\right) d y=0$

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Question 21

21. $(x+y) d y+(x-y) d x=0 ; y=1$ यदि $x=1$

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Question 22

22. $x^2 d y+\left(x y+y^2\right) d x=0 ; y=1$ यदि $x=1$

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Question 23

23. $\left[x \sin ^2\left(\frac{y}{x}\right)-y\right] d x+x d y=0 ; y=\frac{\pi}{4}$ यदि $x=1$

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Question 24

24. $\frac{d y}{d x}-\frac{y}{x}+\operatorname{cosec}\left(\frac{y}{x}\right)=0 ; y=0$ यदि $x=1$

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Question 25

25. $2 x+y^2-2 x^2 \frac{d y}{d x}=0 ; y=2$ यदि $x=1$.