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BT-202 · Mathematics II/Unsolved PYQ Paper

BT-202 Mathematics - II - Dec 2023 Question Paper

  1. 7 Marks
    aSolve $(1 + y^2)dx = (\tan^{-1}y - x)dy$ using Leibnitz linear method.
  2. 7 Marks
    bSolve $(e^y + 1)\cos x dx + e^y \sin x dy = 0$.
  3. 7 Marks
    aSolve $(D^2 - 4D + 3)y = \cos 2x$.
  4. 7 Marks
    bShow that $J_{\frac{1}{2}}(x) = \sqrt{\frac{2}{\pi x}} \sin x$.
  5. 14 Marks
    Solve $(D^2 + 9)y = \tan 3x$ by using method of variation of parameters.
  6. 7 Marks
    aSolve the partial differential equation $(x - y)p + (x + y)q = 2xz$.
  7. 7 Marks
    bSolve $(p^2 + q^2)y = qz$ by using Charpit's method.
  8. 7 Marks
    aSolve $(D^2 + 4DD' - 5D'^2)Z = \sin(2x + 3y)$.
  9. 7 Marks
    bDetermine $p$ so that the function $f(z) = \frac{1}{2}\log(x^2 + y^2) + i\tan^{-1}\left(\frac{px}{y}\right)$ is analytic function.
  10. 7 Marks
    aShow that the function $u(x, y) = e^x \cos y$ is Harmonic. Determine it's Harmonic conjugate.
  11. 7 Marks
    bFind the residue of $\frac{Z e^z}{(Z-1)^3}$ at it's pole.
  12. 14 Marks
    Verify Gauss divergence theorem for $\overline{F} = x^3 \overline{i} + y^3 \overline{j} + z^3 \overline{k}$ taken over the cube bounded by $x = 0$, $x = a$, $y = 0$, $y = a$, $z = 0$, $z = a$.
  13. 7 Marks
    aProve that $\text{curl}(r^n \overline{r}) = \overline{0}$
  14. 7 Marks
    bWrite short note on: i) Cauchy Riemann equations ii) Stokes theorem
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