MCQ
$f(x,\;y) = \frac{1}{{x + y}}$ is a homogeneous function of degree
- A$1$
- ✓$-1$
- C$2$
- D$-2$
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$STATEMENT -1$ : The function $F(x)$ satisfies $F(x+\pi)=F(x)$ for all real $x$. because
$STATEMENT -2$$: \sin ^2(x+\pi)=\sin ^2 x$ for all real $x$.
The general solution of the differential equation $\frac{\text{dy}}{\text{dx}}\ \text{e}^{\frac{\text{x}^2}{2}}+\text{xy}$ is:
$\text{y}=\text{c}\text{e}^{\frac{-\text{x}^2}{2}}$
$\text{y}=\text{c}\text{e}^{\frac{\text{x}^2}{2}}$
$\text{y}=(\text{x}+\text{c})\text{e}^{\frac{\text{x}^2}{2}}$
$\text{y}=(\text{c}-\text{x})\text{e}^{\frac{\text{x}^2}{2}}$