AP EAMCET · Maths · Differential Equations
The general solution of the differential equation \(\frac{d y}{d x}+y g^{\prime}(x)=g(x) g^{\prime}(x)\) is
- A \(g(x)+\log (1+y+g(x))=c\)
- B \(g(x)+\log (1+y-g(x))=c\)
- C \(g(x)-\log (1+y+g(x))=c\)
- D \(g(x)-\log (1+y-g(x))=c\)
Answer & Solution
Correct Answer
(B) \(g(x)+\log (1+y-g(x))=c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \frac{d y}{d x}+y g^{\prime}(x)=g(x) \cdot g^{\prime}(x) \\ & \therefore P=g^{\prime}(x) \text { and } Q=g(x) \cdot g^{\prime}(x) \\ & \text {IF }=e^{\int p d x} \\ & =e^{\int g^{\prime}(x) d x} \\ & \mathrm{IF}=e^{g(x)} \\ \end{aligned}\) General Solution is…
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