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Find the orthogonal trajectory of y^2=4a...

Find the orthogonal trajectory of `y^2=4a x` (a being the parameter).

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CENGAGE PUBLICATION-DIFFERENTIAL EQUATIONS-All Questions
  1. Solve the equation (dy)/(dx)+(x y)/((1-x^2))=xsqrt(y)

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  2. Solve the equation (dy)/(dx)=(x^3-2xtan^(-1)y)(1+y^2)

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  3. Find the orthogonal trajectory of y^2=4a x (a being the parameter).

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  4. Solve [xsin^2(y/x)-y]dx+x dy=0; y=pi/4 when x=1.

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  5. Find the orthogonal trajectories of family of curves x^2+y^2=c x

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  6. Show that the differential equation y^3dy+(x+y^2)dx=0 can be reduced t...

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  7. Solve [2sqrt(x y)-x]dy+ydx=0

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  8. Suppose that a mothball loses volume by evaporation at a rate propo...

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  9. Find the equation of the curve which is such that the area of the rect...

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

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  11. If the population of country double in 50 years, in how many years wil...

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  12. Find the equation of the curve passing through the origin if the middl...

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  13. Find the real value of m for which the substitution y=u^m will transfo...

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  14. A curve y=f(x) passes through point P(1,1) . The normal to the curv...

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  15. Find the equation of a curve passing through (0,1) and having gradient...

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  16. Solve (dy)/(dx)=(x-2y+5)/(2x+y-1)

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  17. Solve x dy=(y+x(f(y/x))/(f^(prime)(y/x)))dx

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  18. Solve the equation ydx+(x-y^2)dy=0

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  19. Find the orthogonal trajectory of y^2=4a x (a being the parameter).

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  20. Solve e^((dy)/(dx))=x+1, given that when x=0,y=3.

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