Question

Find the equation of the solution to dy/dx = x^(5) * y through the point (x;y)=(1;2)

Answer 1

$\frac{dy}{dx}=x⁵y,$ $(x,y)=(1,2)$

$\frac{dy}{y}=x⁵dx$

Integrating both sides, we have;

$lny=\frac{x⁶}{6}+c$

Recall that y(1)=2

$ln2=\frac{1}{6}+c$

$c=ln2-\frac{1}{6}$

$c=0.53$

$lny=\frac{x⁶}{6}+0.53$

$=>y=e^{\frac{x⁶}{6}+0.53}$

$=>y=e^{\frac{x⁶}{6}}e^{0.53}$

$=>y=1.70e^{\frac{x⁶}{6}}$