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#### Ordinary Differential Equations Five Marks Questions

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
10 x 5 = 50
1. Form the differential equation by eliminating the arbitrary constants A and B from y = Acos x + B sin x.

2. Find the differential equation of the family of circles passing through the points (a,0) and (−a,0).

3. Find the differential equation of the family of all ellipses having foci on the x -axis and centre at the origin.

4. Find the particular solution of (1+ x3 )dy − x2 ydx = satisfying the condition y(1) = 2.

5. Solve y ' = sin2 (x − y + )1.

6. Solve : $\frac { dy }{ dx } =\sqrt { 4x+2y-1 }$

7. Solve $\frac { dy }{ dx } =\frac { x-y+5 }{ 2(x-y)+7 } .$

8. Solve [y(1-x tan x)+x2 cosx]dx-dy=0

9. Solve (1+x3)$\frac { dy }{ dx }$+6x2y=1+x2.

10. Solve yeydx=(y3+2xey)dy