WBJEE · Maths · Differential Equations
The equation of one of the curves whose slope at any point is equal to \(\mathrm{y}+2 \mathrm{x}\) is
- A \(y=2\left(e^x+x-1\right)\)
- B \(y=2\left(e^x-x-1\right)\)
- C \(y=2\left(e^x-x+1\right)\)
- D \(y=2\left(e^x+x+1\right)\)
Answer & Solution
Correct Answer
(B) \(y=2\left(e^x-x-1\right)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Hints: } \frac{d y}{d x}=y+2 x \quad \text { Put } y+2 x=z \Rightarrow \frac{d y}{d x}+z=\frac{d z}{d x} \\ & \frac{d z}{d x}-2=z, \quad \frac{d z}{d x}=z+2 \Rightarrow \int \frac{d z}{z+2}=\int d x \\ & \log (z+2)=x+c, \log (y+2 x+2)=x+c \\ & y+2…
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