Final answer to the problem
$\frac{2\arctan\left(\frac{\tan\left(\frac{x+y}{2}\right)}{\sqrt{1+4\tan\left(\frac{x+y}{2}\right)}}\right)}{\sqrt{1+4\tan\left(\frac{x+y}{2}\right)}}=x+C_0$
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Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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
Grouping the terms of the differential equation
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$\frac{dy}{dx}=0+2\sin\left(x+y\right)$
Learn how to solve problems step by step online. Solve the differential equation dy/dx-2sin(x+y)=0. Grouping the terms of the differential equation. x+0=x, where x is any expression. 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 x+y has the form Ax+By+C. Let's define a new variable u and set it equal to the expression. Isolate the dependent variable y.
Final answer to the problem
$\frac{2\arctan\left(\frac{\tan\left(\frac{x+y}{2}\right)}{\sqrt{1+4\tan\left(\frac{x+y}{2}\right)}}\right)}{\sqrt{1+4\tan\left(\frac{x+y}{2}\right)}}=x+C_0$
