Question

Find the solution to the initial value problem (1 + x^{5}) y' + 5 x^{4} y = 5 x^{8}

Answer 1

$(1+x^5)y'+5x^4y=5x^8$
$\bigg((1+x^5)y\bigg)'=5x^8$
$(1+x^5)y=5\displaystyle\int x^8\,\mathrm dx$
$(1+x^5)y=\dfrac59x^9+C$
$y=\dfrac{5x^9+C}{9(1+x^5)}$