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Consider the family of all circles whose...

Consider the family of all circles whose centers lie on the straight line `y=x`. If the family of circles is represented by the differential equation `Py^('')+Qy^(')+1=0`, where P, Q are functions of x, y and `y^(')` (here `y^(')=(dy)/(dx),y^('')=(d^(2)y)/(dx^(2))`, then which of the following statements is (are) true?

A

P=y+x

B

P=y-x

C

P+Q=1-x+y+y'+(y')^(2)`

D

P-Q=x+y-y'-(y')^(2)`

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The correct Answer is:
B, C, D
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ARIHANT MATHS ENGLISH-DIFFERENTIAL EQUATION -Exercise (Questions Asked In Previous 13 Years Exam)
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  2. Let y(x) be a solution of the differential equation (1+e^(x))y^(')+ye^...

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  3. Consider the family of all circles whose centers lie on the straight l...

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  4. The function y=f(x) is the solution of the differential equation (d...

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  5. Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-cons...

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  6. A curve passes through the point (1,(pi)/(6)). Let the slope of the cu...

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  7. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  8. Let f:[0,1]rarrR be a function. Suppose the function f is twice differ...

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  9. Let f:[0,1]rarrR (the set of all real numbers) be a function. Suppose ...

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  10. Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose t...

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  11. If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c...

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  12. Let y^(prime)(x)+y(x)g^(prime)(x)=g(x)g^(prime)(x),y(0),x in R , wher...

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  13. Let f: R to R be a continuous function which satisfies f(x)= int0^xf(...

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  14. Let a solution y=y(x) of the differential equation xsqrt(x^(2)-1) dy-...

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  15. If a curve y=f(x) passes through the point (1,-1) and satisfies the di...

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  16. Let y(x) be the solution of the differential equation (xlogx)(dy)/(dx)...

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  17. Let the population of rabbits surviving at a time t be governed by t...

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  18. At present, a firm is manufacturing 2000 items. It is estimated tha...

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

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  20. If (dy)/(dx)=y+3 and y(0)=2, then y(log2) is equal to

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