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Solve the following differential equatio...

Solve the following differential equations: `(dy)/(dx)=(x+y)/(x-y)`

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To solve the differential equation \(\frac{dy}{dx} = \frac{x+y}{x-y}\), we can follow these steps: ### Step 1: Identify the Type of Differential Equation The given equation is a homogeneous differential equation because it can be expressed in the form \(\frac{dy}{dx} = \frac{f(y/x)}{g(y/x)}\). ### Step 2: Substitute \(y = vx\) Let \(y = vx\), where \(v\) is a function of \(x\). Then, we can differentiate \(y\) with respect to \(x\): \[ ...
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RD SHARMA-DIFFERENTIAL EQUATION-Solved Examples And Exercises
  1. Solve the following differential equations: [xsqrt(x^2+y^2)-y^2]dx + x...

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  2. Solve the following differential equations: y/x cos(y/x)dx-{x/ysin(y/x...

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  3. Solve the following differential equations: (dy)/(dx)=(x+y)/(x-y)

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

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  5. Solve the following differential equations: x y(dy)/(dx)=x^2+y^2

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  6. Solve the following differential equations: y e^(x//y)dx=(x e^(x/y)+y)...

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  7. Solve: (dy)/(dx)=-(x+ycosx)/(1+sinx)

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  8. Solve: (dy)/(dx)+xsin2y=x^3cos^2y

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  9. Solve: (dy)/(dx)+y/x=cos x+(sinx)/x

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  10. Solve: (dy)/(dx)+ytanx=2x+x^2tanxdot

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  11. Solve: (dy)/(dx)+y=cos x-sinx

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  12. Solve: (1+x^2)(dy)/(dx)+2xy-4x^2=0 subject to the initial conditiony(...

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  13. Solve: (dy)/(dx)-2y=cos3x

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

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  15. Solve the following differential equation: y\ dx+xlog(y/x)dy=2x\ dy

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  16. Determine the order and degree of the following differential equation....

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  17. Determine the order and degree of the following differential equation....

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  18. Determine the order and degree of the following differential equation....

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  19. Determine the order and degree of the following differential equation....

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  20. Determine the order and degree of the following differential equation....

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