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

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

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To solve the differential equation \((x + 2y^3) dy = y dx\), we will follow these steps: ### Step 1: Rearranging the Equation First, we will rearrange the equation to isolate \(dx\) and \(dy\): \[ (x + 2y^3) dy = y dx \] Dividing both sides by \(dy\) gives: ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Solve the following differential equations: x(dy)/(dx)+y=x e^x

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  2. If y(t) is a solution of (1+t)(dy)/(dt)-t y=1a n dy(0)=-1 then show ...

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

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  4. Solve each of the following initial value problems: x(dy)/(dx...

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  5. Solve each of the following initial value problems: (dy)/(dx)+(2x)/(...

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  6. Solve the following differential equations: (2x-10 y^3)(dy)/(dx)+y=0

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

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  8. Solve the following differential equations: (dy)/(dx)+ycosx=sinxcosx

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  9. Solve the following differential equations: (x+tany)dy=sin2ydx

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  10. Solve the following differential equations: (dy)/(dx)-y= xe^x

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

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  12. The surface are of a balloon being inflated changes at a constant r...

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

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  14. Suppose the growth of a population is proportional the umber presen...

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  15. A population grows at the rate of 8% per year. How long does it tak...

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  16. Verify that y=log(x+sqrt(x^2+a^2))^2 satisfies the differential equa...

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  17. Verify that y=c e^(t a n-1x) is a solution of differential equatio...

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  18. Show that the differential equation of which y=2(x^2-1)+c e^(-x^2) is ...

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  19. Form the differential equation corresponding to y^2-2a y+x^2=a^2 by el...

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  20. Show that y=A x+B/x ,x!=0 is a solution of the differential equation x...

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