AP EAMCET · Maths · Differential Equations
The differential equation \(y^2 d x+(2 x y-1) d y=0\) is
- A linear in \(y\)
- B not a linear equation
- C a homogenous equation
- D linear in \(\mathrm{x}\)
Answer & Solution
Correct Answer
(D) linear in \(\mathrm{x}\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text {} y^2 d x+(2 x y-1) d y=0 \\ & \Rightarrow \quad \frac{d x}{d y}+\frac{2 x}{y}-\frac{1}{y^2}=0 \\ & \Rightarrow \quad \frac{d x}{d y}+\left(\frac{2}{y}\right) x=\frac{1}{y^2} \end{aligned} \] Which of the form \(\frac{d x}{d y}+P x=Q\) Hence given…
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