JEE Mains · Maths · STD 12 - 9. differential equations
Let \(y=y(x)\) be the solution of the differential equation \((x+1) y^{\prime}-y=e^{3 x}(x+1)^{2}\), with \(y(0)=\frac{1}{3}\). Then, the point \(x=-\frac{4}{3}\) for the curve \(y = y ( x )\) is
- A not a critical point
- B a point of local minima
- C a point of local maxima
- D a point of inflection
Answer & Solution
Correct Answer
(B) a point of local minima
Step-by-step Solution
Detailed explanation
\((x+1) d y-y d x=e^{3 x}(x+1)^{2}\) \(\frac{(x+1) d y-y d x}{(x+1)^{2}}=e^{3 x}\) \(d\left(\frac{y}{x+1}\right)=e^{3 x} \Rightarrow \frac{y}{x+1}=\frac{e^{3 x}}{3}+C\) \(\left(0, \frac{1}{3}\right) \Rightarrow C=0 \Rightarrow y=\frac{(x+1) e^{3 x}}{3}\)…
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