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If C is an arbitrary constant , then the...

If C is an arbitrary constant , then the general solution of the differential equation ` y dx - x dy = xy dx ` is given by

A

` y = Cxe^(-x)`

B

` y = Cye^(-x)`

C

` y + e^(x) = Cx`

D

` ye^(x) = Cx`

Text Solution

Verified by Experts

The correct Answer is:
d
Given , ` y (1-x) dx = xdy `
` rArr (1/x -1) dx = 1/y dy `
` rArr log (x) - x log y - log C` [ integrating ]
` rArr x = log. (xC)/y rArr ye^(x) = xC`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIAL EQUATION-PRACTICE EXERCISE (Exercise 2 )
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  2. The general solution of the differential equaiton (1+y^(2))dx+(1+x^(2)...

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  3. The solution of (dy)/(dx)+1 = e^(x+y) is

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  4. The differential equation (dy)/(dx) = (x(1+y^(2)))/(y(1+x^(2)) repres...

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  5. If xsin((y)/(x))dy=[ysin((y)/(x))-x]dx ad y(1)=(pi)/(2), then the valu...

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  6. Solution of the differential equation tan y.sec^(2) x dx + tan x. sec^...

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  7. The solution of e^(dy//dx) = (x+1) , y (0) = 3 is

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  8. Solution of the differential equation x((dy)/(dx))^(2)+2sqrt(xy)(dy)...

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  9. If C is an arbitrary constant , then the general solution of the diffe...

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  10. Find the differential equation of system of cocentric circles with cen...

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  11. If a curve passes through the point (2,7/2) and has slope (1-1/(x^(2)...

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  12. The population p(t) at time t of a certain mouse species satisfies the...

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  13. The population p(t) at time t of a certain mouse species satisfies the...

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  14. If (dy)/(dx)=y+3 and y(0)=2, then y(ln 2) is equal to

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  15. Let I be the purchase value of an equipment and V(t) be the value afte...

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  16. Find the equation of the curve in which the perpendicular from the ori...

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  17. The volume of spherical balloon being inflated changes at a constan...

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  18. The order and degree of the differetnial equation sqrt(sin x) (dx+dy...

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  19. The equation of curve in which portion of y-axis cutoff between origin...

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  20. A normal at any point (x,y) to the curve y = f(x) cuts triangle of uni...

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