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Solve each of the following initial valu...

Solve each of the following initial value problem: `x(x^2+3y^2)dx+y(y^2+3x^2)dy=0,\ y(1)=1`

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To solve the initial value problem given by the differential equation: \[ x(x^2 + 3y^2)dx + y(y^2 + 3x^2)dy = 0, \quad y(1) = 1 \] we will follow these steps: ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Solve: (dy)/(dx) = (y ( x + 2y))/(x ( 2x + y)) ,y(1) = 2

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

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

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  4. Solve the following initial value problem: {xsin^2(y/x)-y}dx+x dy=0,\ ...

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  5. Solve the initial value problem: x\ (dy)/(dx)-y+xsin(y/x)=0,\ y(2)=x

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  6. Find the particular solution of the differential equation xcos(y/x)...

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  7. Find the particular solution of the differential equation (x-y)(dy)/(d...

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

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  9. Solve the differential equation : (dy)/(dx)-y/x=2x^2

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  10. Find the general solution of the differential equations: xlogx(dx)/...

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

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  12. Solve: dy / dx + y secx = tanx

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  13. Solve the following differential equation: cos^2x(dy)/(dx)+y=tanx

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  14. Find the general solution of the differential equations: x(dx)/(dy)...

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  15. Find the general solution of the differential equations: (1+x^2)dy+...

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  16. If y+d/(dx)(x y)=x(sinx+logx),fin dy(x)dot

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  17. Solve: y\ dx-(x+2y^2)dy=0

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  18. Solve: y dx + ( x - y^3) dy = 0

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  19. Solve [(e^(-2sqrt(x)))/(sqrt(x))-y/(sqrt(x))](dx)/(dy)=1(x!=0)

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  20. Solve each of the following initial value problem: (x-siny)dy+(tan...

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