Question

If function $y=f\left(x\right)$ satisfies $(x+1)$ $f\left(x\right)-2(x^2+x)f\left(x\right)=\frac{e^{x^2}}{(x+1)},\forall x>-1$

• A. $\left(\frac{3x+5}{x+1}\right)e^{x^2}$
• B. $\left(\frac{6x+5}{x+1}\right)e^{x^2}$
• C. $\left({\frac{6x+5}{(x+1)}}^2\right)e^{x^2}$
• D. None of these

Answer 1

Answer: (D)

None of these

$\begin{array}{c}\left(x+1\right)f\left(x\right)-2\left(x^2+x\right)f\left(x\right)=\frac{e^{x^2}}{x+1}\forall -1\\ f\left(x\right)\left[x+1-2x^2-2x\right]=\frac{e^{x^2}}{x+1}\\ f\left(x\right)\left[-2x^2-x+1\right]=\frac{e^{x^2}}{x+1}\\ f\left(x\right)=\frac{e^{x^2}}{\left(x+1\right)\left(x+1\right)\left(-2x+1\right)}\end{array}$