TS EAMCET · Maths · Differential Equations
The solution of \(\frac{d y}{d x}+\frac{1}{3} y=1\) is
- A \(y=3+c e^{x / 3}\)
- B \(y=3+c e^{-x / 3}\)
- C \(3 y=c+e^{x / 3}\)
- D \(y^2+x+x^2+2=c e^{2 x}\)
Answer & Solution
Correct Answer
(B) \(y=3+c e^{-x / 3}\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{array}{rlrl} & \quad \frac{d y}{d x}+\frac{y}{3} & =1 \\ \Rightarrow & & d y & =-\frac{(y-3)}{3} d x \\ \Rightarrow & \frac{d y}{y-3} & =-\frac{1}{3} d x \end{array} \]…
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