TS EAMCET · Maths · Differential Equations
Consider the differential equation \(\frac{d y}{d x}=\frac{1}{a x+4 y+7}\) and the following statements A. The given differential equation is linear in \(x\). \(B\). The given differential equation is not linear in \(y\). C. The given differential equation is linear in \(y\). D. \(e^{a x}\) is the integrating factor of the given differential equation. Which one of the following options is true?
- A Only C and D are true
- B Only B and D are true
- C Only B and A are true
- D Only A and C are true
Answer & Solution
Correct Answer
(C) Only B and A are true
Step-by-step Solution
Detailed explanation
We have, \(\frac{d y}{d x}=\frac{1}{a x+4 y+7}\) \(\Rightarrow \quad \frac{d x}{d y}=a x+4 y+7 \Rightarrow \frac{d x}{d y}-a x=4 y+7\) Which is form of \(\frac{d x}{d y}+P x=Q\) \(\therefore\) Differential equation is linear in \(x\) but not linear in \(y\)…
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