Final answer to the problem
$\frac{\tan\left(y\right)\sec\left(y\right)}{2}+\frac{1}{2}\ln\left|\sec\left(y\right)+\tan\left(y\right)\right|=-3\left(\frac{1}{3}e^x\sin\left(2x\right)-\frac{2}{3}e^x\cos\left(2x\right)\right)$
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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
Learn how to solve trigonometric integrals problems step by step online.
$\frac{dy}{dx}=\frac{\left(e^x\tan\left(y\right)^2+e^x\right)\sin\left(2x\right)\cos\left(y\right)^5}{3}$
Learn how to solve trigonometric integrals problems step by step online. Solve the differential equation 3dy/dx=(e^xtan(y)^2+e^x)sin(2x)cos(y)^5. Rewrite the differential equation. Factoring by e^x. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression \frac{1}{1+\tan\left(y\right)^2}\frac{1}{\cos\left(y\right)^5}dy.
Final answer to the problem
$\frac{\tan\left(y\right)\sec\left(y\right)}{2}+\frac{1}{2}\ln\left|\sec\left(y\right)+\tan\left(y\right)\right|=-3\left(\frac{1}{3}e^x\sin\left(2x\right)-\frac{2}{3}e^x\cos\left(2x\right)\right)$
