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कृपया अपनी पसंदीदा भाषा चुनें
यदि $\frac{d x}{d y}=\frac{1+x-y^{2}}{y}, x(1)=1$, तो $5 x(2)$ के बराबर है :
$\frac{d x}{d y}-\frac{x}{y}=\frac{1-y^{2}}{y}$
समाकलन गुणक $=e^{\int-\frac{1}{y} d y}=\frac{1}{y}$
$x \cdot \frac{1}{y}=\int \frac{1-y^{2}}{y^{2}} d y$
$\frac{x}{y}=\frac{-1}{y}-y+c$
$x=-1-y^{2}+c y$
दिया गया है $x(1)=1$
$1=-1-1+c \Rightarrow c=3$
$x=-1-y^{2}+3 y$
$5 x(2)=5(-1-4+6)$
$=5$
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