# Solve differential equation x'(t)= \frac{\sin (t)}{x^2(t)+1}

Lennie Carroll 2021-01-15 Answered
Solve differential equation ${x}^{\prime }\left(t\right)=\frac{\mathrm{sin}\left(t\right)}{{x}^{2}\left(t\right)+1}$
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Faiza Fuller
$\frac{dx}{dt}=\frac{\mathrm{sin}t}{{x}^{2}\left(t\right)+1}$
$\int \left({x}^{2}+1\right)dx=\int \mathrm{sin}tdt$
$\frac{{x}^{3}}{3}+x=-\mathrm{cot}t+c$
$\frac{{x}^{3}\left(t\right)}{3}+x\left(t\right)=-\mathrm{cot}t+c$