Final answer to the problem
$\frac{\cos\left(\theta\right)-\sin\left(\theta\right)-\cos\left(\theta\right)^{4\theta}}{\cos\left(\theta\right)}=\sin\left('''\theta\right)^{\prime}-\tan\left(\theta\right)$
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Step-by-step Solution
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- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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1
Rewrite the differential equation using Leibniz notation
$\frac{\cos\left(\theta\right)-\sin\left(\theta\right)-\cos\left(\theta\right)^{4\theta}}{\cos\left(\theta\right)}=\sin\left('''\theta\right)^{\prime}-\tan\left(\theta\right)$
Final answer to the problem
$\frac{\cos\left(\theta\right)-\sin\left(\theta\right)-\cos\left(\theta\right)^{4\theta}}{\cos\left(\theta\right)}=\sin\left('''\theta\right)^{\prime}-\tan\left(\theta\right)$