Differential Equations Maths - Differential Equations

• ✓
  $\sin\frac{\text{x}}{\text{y}}=\text{x}+\text{C}$
• B
  $\sin\frac{\text{y}}{\text{x}}=\text{Cx}$
• C
  $\sin\frac{\text{x}}{\text{y}}=\text{Cy}$
• D
  $\sin\frac{\text{y}}{\text{x}}=\text{Cy}$

Answer: A.

• A
  $\frac{1}{2}$
• ✓
  $2$
• C
  $3$
• D
  $4$

Answer: B.

• A
  $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-\text{x}^{2}\frac{\text{dy}}{\text{dx}}+\text{xy}=\text{x}$
• B
  $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\text{x}^{2}\frac{\text{dy}}{\text{dx}}+\text{xy}=\text{x}$
• ✓
  $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}-\text{x}^{2}\frac{\text{dy}}{\text{dx}}+\text{xy}=\text{0}$
• D
  $\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}+\text{x}^{2}\frac{\text{dy}}{\text{dx}}+\text{xy}=\text{0}$

Answer: C.

• ✓
  $\text{y}=\text{xe}^{\text{x}+\text{C}}$
• B
  $\text{x}=\text{ye}^{\text{x}}$
• C
  $\text{y}=\text{x}+\text{c}$
• D
  $\text{xy}=\text{e}^{\text{x}}+\text{C}$

Answer: A.

• A
  y = vx
• B
  v = yx
• ✓
  x = vy
• D
  x = v

Answer: C.