Final answer to the problem
$2\cdot \left(\frac{1}{\sqrt{3}}\right)\arctan\left(\frac{\tan\left(\frac{2x+y+3}{2}\right)}{\sqrt{3}}\right)=x+C_0$
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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
Divide both sides of the equation by $dx$
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$\frac{dy}{dx}=\frac{dx}{dx}\cos\left(2x+y+3\right)$
Learn how to solve problems step by step online. Solve the differential equation dy=cos(2x+y+3)dx. Divide both sides of the equation by dx. Simplify the fraction \frac{dx}{dx} by dx. Any expression multiplied by 1 is equal to itself. When we identify that a differential equation has an expression of the form Ax+By+C, we can apply a linear substitution in order to simplify it to a separable equation. We can identify that 2x+y+3 has the form Ax+By+C. Let's define a new variable u and set it equal to the expression.
Final answer to the problem
$2\cdot \left(\frac{1}{\sqrt{3}}\right)\arctan\left(\frac{\tan\left(\frac{2x+y+3}{2}\right)}{\sqrt{3}}\right)=x+C_0$
