If d x/d y=frac 1+x-y 2 y , x(1)=1 , then 5 x(2) is equal to :

Mathematics · Differential Equations

JEE Main 2024 — 1 February, Shift 2 — Question 29

If $\frac{d x}{d y}=\frac{1+x-y^{2}}{y}, x(1)=1$ , then $5 x(2)$ is equal to :

Numerical answer — enter this value.

$\frac{d x}{d y}-\frac{x}{y}=\frac{1-y^{2}}{y}$

Integrating factor $=e^{\int-\frac{1}{y} d y}=\frac{1}{y}$

$x \cdot \frac{1}{y}=\int \frac{1-y^{2}}{y^{2}} d y$

$\frac{x}{y}=\frac{-1}{y}-y+c$

$x=-1-y^{2}+c y$

$\mathrm{x}(1)=1$

$1=-1-1+\mathrm{c} \Rightarrow \mathrm{c}=3$

$x=-1-y^{2}+3 y$

$5 x(2)=5(-1-4+6)=5$

Answer key and solution verified before publishing.

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