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Solve any one of the following.
Solve the differential equation: (x + 5y²)(dy)/(dx) = y when x = 2 and y = 1
Solve the differential equation:
$(x + 5y^2)\frac{dy}{dx} = y$ when $x = 2$ and $y = 1$
Answer
Answer
$(x+5y^2)\frac{dy}{dx}=y\Rightarrow\frac{dx}{dy}-\frac xy=5y$ (linear in $x$).
Integrating factor $=e^{-\int dy/y}=\frac1y$.
$\frac xy=\int5\,dy=5y+C$.
At $x=2,y=1$: $2=5+C$, so $C=-3$.
Hence $x=5y^2-3y$.
Final answer: $x=5y^2-3y$