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Solve the differential equation: `(1+y+x^2y)dx+(x+x^3)dy=0`

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To solve the differential equation \((1+y+x^2y)dx+(x+x^3)dy=0\), we will follow these steps: ### Step 1: Rewrite the Equation We start with the given differential equation: \[ (1 + y + x^2y)dx + (x + x^3)dy = 0 \] Rearranging gives: ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Solve the differential equation: (dy)/(dx)-\ ycot\ x=cos e c\ x

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  2. Solve the following differential equation: (dy)/(dx)-\ ytanx=e^xsecx

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  3. Solve the differential equation: (1+y+x^2y)dx+(x+x^3)dy=0

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  4. Solve the differential equation: y \ sec^2x+(y+7)\tanx(dy)/(dx)=0

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  5. Solve the following differential equation: (x^3-2y^3)dx+3x^2y\ dy=0

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  6. Solve the following differential equation: y-x(dy)/(dx)=b\ (1+x^2 \ (d...

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  7. Solve the following differential equation: (dy)/(dx)+\ y=4x

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  8. Solve the following differential equation: \ x(dy)/(dx)=y-xcos^2(y/x)

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  9. solution of differential equation xcosx(dy)/(dx)+y(xsinx+cosx)=1 is

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  10. Solve the differential equation: y^2+(x-1/y)(dy)/(dx)=0\

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  11. Solve the differential equation: 2cosx(dy)/(dx)+4y\ sin x=sin2x ,given...

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  12. Solve the differential equation: (1+y^2)dx=(tan^(-1)y-x)dy

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  13. Solve the following differential equation: x\ (e^(2y)-1)dy+(x^2-1)e^y ...

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  14. Solve the differential equation dy/dx + y/x = y^2/x^2

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  15. Solve the following differential equation: (x+y-1)dy=(x+y)dx

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  16. Solve the following differential equations: (dy)/(dx)=ytanx-2sinx

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  17. Solve the following differential equation: (dy)/(dx)-ytanx=e^xsecx

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  18. Solve the following differential equation: (x^2+1)dy+(2y-1)dx=0

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  19. Solve the differential equation: (2a x+x^2)\ (dy)/(dx)=a^2+2a x

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  20. Solve the following differential equation: x^2dy+(x^2-x y+y^2)dx=0

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