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Solve: x^2ydx=(x^3+y^3)dy=0...

Solve: `x^2ydx=(x^3+y^3)dy=0`

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To solve the differential equation \( x^2 y \, dx = (x^3 + y^3) \, dy = 0 \), we can follow these steps: ### Step 1: Rewrite the differential equation We can express the equation in the form of a ratio: \[ \frac{dy}{dx} = \frac{x^2 y}{x^3 + y^3} \] ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Solve the following differential equations: (dy)/(dx)+1=e^(x+y)

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  2. Solve: (x^3-3x y^2)dx=(y^3-3x^2y)dydot

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  3. Solve: x^2ydx=(x^3+y^3)dy=0

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  4. Solve the following differential equations: (x+y)^2(dy)/(dx)=1

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  5. Solve the following differential equations: (dy)/(dx)=((x-y)+3)/(2(x-y...

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  6. Solve the following differential equations: (x+y+1)(dy)/(dx)=1

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  7. Solve the following differential equations: (x+y)(dx-dy)=dx+dy

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  8. Solve x (dy)/(dx)sin(y/x)+x-ysin(y/x)=0 given y(1)=pi/2

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  9. Solve: x(dy)/(dx)=y-xtan(y/x)dot

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  10. A thermometer reading 80^@F is taken outside. Five minutes later the t...

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  11. The doctor took the temperature of a dead body at 11.30 Pm which was 9...

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  12. If is given that radium decomposes at a rate proportional to the am...

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  13. A radioactive substance disintegrates at as rate proportional to the...

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  14. If is known that, if the interest i s compounded continuously, the ...

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  15. Bacteria multiply at a rate proportional to the number present. If the...

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  16. A spherical rain drop evaporates at a rate proportional to its surf...

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  17. Water at temperature 100^@C cools in 10 minutes to 88^@C in a room of ...

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  18. Solve the following differential equations: (dy)/(dx)=sin^3xcos^2x+x ...

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  19. Solve: (dy)/(dx)=1/(sin^4x+cos^4x)

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  20. Solve the initial value problem e^((dy//dx))=x+1; y(0)=5.

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