अवकल समीकरण गणित - अवकल समीकरण

• A
  $\frac{x^2}{2}-\frac{y^2}{2}=x+y+c$
• B
  $x-y=\log (x+y)+c$
• ✓
  $\frac{x^2}{2}-\frac{y^2}{2}+x y=x+y+c$
• D
  $x+y=\log (x-y)+c$

Answer: C.

• A
  $x+y=k(1-x y)$
• B
  $y-x=k(1-x y)$
• C
  $x+y=k(1+x y)$
• ✓
  $y-x=k(1+x y)$ Ans.

Answer: D.

• A
  $e^{\int P d x}$
• ✓
  $e^{\int P d y}$
• C
  $e^{\int Q d x}$
• D
  $e^{\int Q d y}$

Answer: B.

• A
  $\frac{x^2}{2}+\frac{y^2}{2}+\log \left(x^2+y^2\right)+c$
• ✓
  $\frac{x^2}{2}+\frac{y^2}{2}+\log \left(x^2-y^2\right)+c$
• C
  $\frac{x^2}{2}+\frac{y^2}{2}+\tan ^{-1} \frac{x}{y}+c$
• D
  $\frac{x^2}{2}+\frac{y^2}{2}+\tan ^{-1} \frac{y}{x}+c$

Answer: B.

• A
  $\log 2$
• ✓
  $\frac{1}{4} \log 2$
• C
  $-\frac{1}{4} \log 2$
• D
  $4 \log 2$

Answer: B.

• A
  $xe^y+ y^2 = C$
• ✓
  $ye^x+ x^2 = C$
• C
  $ye^y+ x^2 = C$
• D
  $xe^y + x^2 = C$

Answer: B.