Please help with $8$ and $10.$

Solve the differential equation.

$\frac{du}{(d)t}=21+3u+7t+ut$

a$)u=-7+C{e}^{\frac{x^2}{2}+3t}$

b$)u=-7+C{e}^{t^2-3t}$

c$)u=-7+C{e}^{\frac{t^2}{2}-3t}$

d$)u=-7+C{e}^{t^2+3t}$

$u=-7+C{e}^{\frac{t^2}{2}+3t^2}$

Question $9(1$ point$)$ Saved

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Solve the differential equation.

$y^{\text{'}}=\frac{6x^{5}y}{ln(y)}$

a$)y=3e^{+-\sqrt[\phantom{2}]{2x^6+c}}$

b$)y=e^{+-\sqrt[\phantom{2}]{2x^6+C}}$

c$)y=e^{+-\sqrt[\phantom{2}]{2x^6}}$

d$)y=e^{+-\sqrt[\phantom{2}]{2x+C}}$

Question $10(1$ point$)$

Solve the differential equation.

$(4+t)\frac{du}{(d)t}+u=4+t$;$t>0$

a$)u=\frac{0\mathrm{.}5t^2+C}{4+t}$

b$)u=\frac{4t+0\mathrm{.}5t^2+C}{4+t}$

c$)u=\frac{4t+0\mathrm{.}5t^2}{4+t}$

d$)u=\frac{4t+0\mathrm{.}5t^2+C}{t}$