TS EAMCET · Maths · Differential Equations
The general solution of the differential equation \(\frac{d y}{d x}=\frac{x+7 y+3}{3 x+5 y+9}\) is
- A \((x-3)^4(y-x+3)^4=c(5 y+x-3)^5\)
- B \((x+3)^4(y-x-3)^4=c(5 y+x+3)^5\)
- C \((y-x+3)^4=c|5 y+x-3|\)
- D \((y-x+3)^4=c|5 y+x+3|\)
Answer & Solution
Correct Answer
(C) \((y-x+3)^4=c|5 y+x-3|\)
Step-by-step Solution
Detailed explanation
We have, \(\frac{d y}{d x}=\frac{x+7 y+3}{3 x+5 y+9}\) Put, \(x=x+h\) and \(y=y+k\) \(\therefore \quad \frac{d y}{d x}=\frac{(x+7 y)+(h+7 k+3)}{(3 x+5 y)+(3 h+5 k+9)}\) Put \(h+7 k+3=0\) and \(3 h+5 k+9=0\) \(\Rightarrow \quad h=-3, k=0\)…
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