COMEDK · Maths · 32. Differential Equations
The general solution of \(\frac{d y}{d x}=1+x+y+x y\), \(y=\)
- A \(k e^{x+\frac{x^2}{2}}-1\)
- B \(k e^{x-\frac{x^2}{2}}+1\)
- C \(k e^{1+\frac{x^2}{2}}-1\)
- D \(k e^{1-\frac{x^2}{2}}+1\)
Answer & Solution
Correct Answer
(A) \(k e^{x+\frac{x^2}{2}}-1\)
Step-by-step Solution
Detailed explanation
We have, \(\begin{aligned} & \frac{d y}{d x}=1+x+y(1+x) \\ & \frac{d y}{d x}=(1+x)(1+y) \\ & \frac{d y}{1+y}=(1+x) d x \end{aligned}\) \(\therefore\) Integrate both sides,…
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