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Solve each of the following initial valu...

Solve each of the following initial value problems: `(dy)/(dx)+(2x)/(x^2+1)y=1/((x^2+1)^2),y(0)=0` (ii) `(x^2+1)y -2x y=(x^4+2x^2+1)cosx ,y(0)=0`

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The correct Answer is:
`y=(x^(2)+1)sinx `
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MODERN PUBLICATION-DIFFERENTIAL EQUATIONS-Revision Exercise
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  3. Find the equation of a curve passing through the point (1, 1), given t...

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  4. The decay rate of radium at any time t is proportional to its mass ...

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  5. Solve : (dy)/(dx)= (2x+3y-4)^(2).

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  6. Solve: (dy)/(dx)+y=e^x

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

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  8. Solve: (dy)/(dx) = (y ( x + 2y))/(x ( 2x + y)) ,y(1) = 2

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  9. Solve each of the following initial value problem: (y^4-2x^3y)dx+(x^4-...

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  10. Solve each of the following initial value problem: x(x^2+3y^2)dx+y(y^2...

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

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  12. If ye^(y) dx = (y^(3) + 2xe^(y))dy, y(0) = 1, then the value of x when...

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

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  14. Find the particular solution of the differential equation. (dy)/(dx...

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  15. Find the particular solutions of : (1+xy)y dx + (1-xy)x dy = 0, y(1)...

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  16. The rate of increase in the number of bacteria in a certain bacteri...

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  17. The population of a city increases at a rate proportional to the numbe...

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  18. Assume that the rate at which radioactive nuclei decay is proportioanl...

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  19. If the interest is compounded continuously at 6% per annum, how muc...

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  20. A thermometer reading 80^0F is taken outside. Five minutes later the ...

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