Is it possible to solve an equation such as $$ \left(\frac{\mathrm{d}\theta}{\mathrm{d}t}\right)^2+\frac{\mathrm{d}\theta}{\mathrm{d}t}+y=0 $$ for $\frac{\mathrm{d}\theta}{\mathrm{d}t}$
Solve $\left(\frac{\mathrm{d}\theta}{\mathrm{d}t}\right)^2+\frac{\mathrm{d}\theta}{\mathrm{d}t}+y=0$
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calculus
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0That is quadratic in $\theta '$. – 2017-01-10
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1Replace the word 'derivative' with a variable and you recover a high school problem. – 2017-01-10
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1Is y a function of $t$ or $\theta$? – 2017-01-10
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2are you sure you really mean $$\left( \frac{d\theta}{dt} \right)^2 + \frac{d\theta}{dt} + y = 0$$ and not $$\frac{d^2 \theta}{dt^2}+ \frac{d\theta}{dt} + y = 0?$$ – 2017-01-10
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0Do you just want to find an expression for the derivative? – 2017-01-10
1 Answers
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Yes. It is a simple second degree equation: Put $x=d \theta/ dt$ and solve: $$ x^2+x+y=0 $$