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Solve the following differential equatio...

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

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$$ 3 x^{2} d y=\left(3 x y+y^{2}\right) d x $$ $$ \frac{d y}{d x}=\frac{3 x y+y^{2}}{3 x^{2}} \ldots \ldots . .(1) $$ Let `y=t x` ,Then, `\frac{d y}{d x}=t \frac{d t}{d x}`
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Solve the following differential equation: x^2(dy)/(dx)=x^2-2y^2+x y

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

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

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

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  5. Solve x((dy)/(dx))=y(logy-logx+1)

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

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

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  8. Solve the following differential equation: x(dy)/(dx)-y+xsin(y/x)=0

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  9. Solve each of the following initial value problem: (x^2+y^2)dx=2x y\ d...

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  10. Solve each of the following initial value problem: x e^(y//x)-y+x(dy)/...

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  11. Solve each of the following initial value problem: (dy)/(dx)-y/x+cos e...

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  12. Solve each of the following initial value problem: (x y-y^2)dx+x^2dy=0...

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

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

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

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

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

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

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

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

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