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R23 (UNIT - 2) (JNTU K) DE & VC SHORT ANSWER QUEESTIONS

6. VERIFICATION OF GREEN'S THEOREM

R23 DE & VC UNIT 1 VSAQS PART A(2M)

39. PROBLEMS ON NATURAL GROWTH LAW.

38. PROBLEMS ON NATURAL GROWTH LAW (BACTERIA PROBLEMS)

37. STATEMENT OF NATURAL GROWTH & DECAY LAWS.

36. NEWTON'S LAW OF COOLING - EXAMPLE.

8. BERNOULLI'S EQUTIONS - PROCEDURE TO REDUCE IT TO LINEAR DIFFERENTIAL EQUATION.

9. SOLVE x.dy/dx + y = x³y⁶.

11. SOLVE xy(1+ xy²)dy/ dx = 1.(BERNOULLI'S IN 'X').

7 SOLVE (x + 1 )dy/dx - y = e³ˣ( x+ 1 )².

6. SOLVE (1 + y²) + ( x - exp(tan⁻¹y))dy/dx = 0.( linear in x).

5. SOLVE (1 + y² )dx = (tan⁻¹y - x )dy.( LINEAR DIFFERENTIAL EQUATIONS IN 'X)'.

4. SOLVE xcosx dy/dx + ( xsinx + cosx) y = 1.

3. SOLVE dy / dx + y/ xlogx = sin2x/ logx. (LINEAR DIFFERENTIAL EQUATIONS)

2. Solve ( 1 - x² ) dy/dx + xy = ax.( Linear D. E.).

1. DIFFERENTIAL EQUATIONS OF FIRST ORDER --- INTRODUCTION.

8. Show that (b - a) / 1+b² ‹ tan-¹b - tan-¹a ‹ (b - a)/1+a² using Lagrange's mean value theorem.

7. STAEMENT OF LAGRANGE'S MEAN VALUE THEOREM and verify for logx on [ 1,e ].

6. VERIFY THE ROLLE'S THEOREM FOR THE FUNCTION log(x²+ab / x(a+b) ) on (a , b).

5. VERIFY THE ROLLE'S THEOREM FOR THE FUNCTION (x + 2)³(x - 3)⁴ on ( -2 3).

3. VERIFY THE ROLLE'S THEOREM FOR THE FUNCTION x(x+3)e⁻ˣ/² on (-3 0).

2.STATEMENT OF ROLLE'S THEREOM AND EXAMPLE

R23 JNTU K MATHS : 1. INTRODUCTION TO CALCULUS (MEAN VALUE THEOREMS)