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Show that y=acos(logx)+bsin(logx) is a s...

Show that `y=acos(logx)+bsin(logx)` is a solution of the differential equation `x^2(d^2y)/(dx^2)+(dy)/(dx)+y=0.`

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RD SHARMA ENGLISH-DIFFERENTIAL EQUATION-All Questions
  1. Show that the function y=(A+B x)e^(3x) is a solution of the equation (...

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  2. Show that y=c x+a/c is a solution of the differential equation y=x(dy)...

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  3. Show that y=acos(logx)+bsin(logx) is a solution of the differential eq...

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  4. Solve the following differential equations: (x^2+y^2)(dy)/(dx)=8x^2-3x...

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  5. Solve the following differential equations: (x^2+3x y+y^2)dx-x^2dy=0

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

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  7. Solve the following differential equations: (dy)/(dx)=y/x-sqrt((y^2)/(...

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  8. Solve the following differential equations: [xsqrt(x^2+y^2)-y^2]dx + x...

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

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

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

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

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

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

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

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

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

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

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

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

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