Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Differential Equations

Short Answer Type

61. Form the differential equation representing the family of curves y = a cos (x + b) where a and b are arbitrary constants.

104 Views

62. Find the differential equation of the family of curves y = A sin mx + B cos mx. where m is fixed, and A and B are arbitrary constants.

90 Views

63. Form the differential equation corresponding to y² = m (a² – x²) by eliminating m and a.

The given equation is $straight y squared space equals space straight m left parenthesis straight a squared minus straight x squared right parenthesis$ ...(1)
Differentiating w.r.t.x, we get,
$2 straight y dy over dx space equals space straight m left parenthesis 0 minus 2 space straight x right parenthesis$
or $straight y dy over dx space equals space minus straight m space straight x$ ...(2)
Again differentiating w.r.t.x,
$straight y fraction numerator straight d squared straight y over denominator dx squared end fraction plus dy over dx. dy over dx space equals space minus straight m$
or $straight y space fraction numerator straight d squared straight y over denominator dx squared end fraction plus open parentheses dy over dx close parentheses squared space equals space minus open parentheses straight y fraction numerator begin display style dy over dx end style over denominator straight x end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space space of space space left parenthesis 2 right parenthesis close square brackets$
or $xy fraction numerator straight d squared straight y over denominator dx squared end fraction plus straight x open parentheses dy over dx close parentheses squared space equals space straight y dy over dx$
Which is the required differential equation.