AP EAMCET · Maths · Differential Equations
The solution of the differential equation \(e^x y d x+e^x d y+x d x=0\) is
- A \(e^x+y x^2=c\)
- B \(2 y e^x+x^2=c\)
- C \(y e^x+x^2 e^y=c\)
- D \(e^x+x e^y=c\)
Answer & Solution
Correct Answer
(B) \(2 y e^x+x^2=c\)
Step-by-step Solution
Detailed explanation
\(e^x y d x+e^x d y+x d x=0\) \(\Rightarrow\left(e^x y+x\right) d x+e^x d y=0 \Rightarrow \frac{d y}{d x}+y=-x e^{-x}\) I.F. \(=e^{\int d x}=e^x\) Solution : \(\begin{aligned} & y e^x=\int-x d x+C_1 \Rightarrow y e^x=\frac{-x^2}{2}+C_1 \\ & 2 y e^x+x^2=C \end{aligned}\)
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