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Find the particular solution of the differential equation `(1+e^(2x))dy+(1+y^2)e^x dx=0,` given that `y=1` when `x=0.`

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To find the particular solution of the differential equation \[ (1 + e^{2x}) dy + (1 + y^2)e^x dx = 0 \] given that \( y = 1 \) when \( x = 0 \), we can follow these steps: ...
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RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
  1. Find the general solution of the differential equations sec^2xtany ...

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  2. Solve: e^xsqrt(1-y^2)dx+y/x dy=0

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  3. Find the particular solution of the differential equation (1+e^(2x))dy...

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  4. Solve the differential equation: (1+y^2)(1+logx)dx+x dy=0 given that w...

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

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  6. Solve: (x^2-y x^2)dy+(y^2+x^2y^2)dx=0 given that, y=1, when x=1

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  7. Solve : 3e^xtany dx+(1-e^x)sec^2y\ dy=0

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  8. Solve: sin^3x(dx)/(dy)=siny

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  9. Solve the differential equation(dy)/(dx)+sqrt((1-y^2)/(1-x^2))=0

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  10. The solution of the differential equation dy/dx=e^(x-y)+x^2e^(-y) is ...

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  11. Solve: (dy)/(dx)=(1+y^2)/(1+x^2)

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  12. Find dy/dx if y= x.tanx .

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  13. Solve the initial value problem: (x+1)(dy)/(dx)=2e^(-y)-1,\ y(0)=0

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  14. Solve the initial value problem: y-x(dy)/(dx)=2(1+x^2(dy)/(dx)),\ y(1)...

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  15. Show that the general solution of the differentia equation (dy)/(dx)...

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  16. Solve the following differential equation log ((dy)/(dx))=3x+4y

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  17. In a bank, principal increases continuously at the rate of 5% per y...

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  18. Find the equation of the curve passing through the point (0, -2) gi...

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  19. At any point (x, y) of a curve, the slope of the tangent is twice t...

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  20. Solve the following differential equation: (x+1)(dy)/(dx)=2x y

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