Final answer to the problem
$\frac{\sqrt{2}}{2\sqrt{3}}\arctan\left(\frac{\sqrt{3}}{\sqrt{2}}\tan\left(\frac{x-y+5}{2}\right)\right)=x+C_0$
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Step-by-step Solution
How should I solve this problem?
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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 $dx$
Learn how to solve integral calculus problems step by step online.
$\frac{dy}{dx}=\frac{dx}{dx}\cos\left(x-y+5\right)$
Learn how to solve integral calculus problems step by step online. Solve the differential equation dy=cos(x-y+5)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 x-y+5 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
$\frac{\sqrt{2}}{2\sqrt{3}}\arctan\left(\frac{\sqrt{3}}{\sqrt{2}}\tan\left(\frac{x-y+5}{2}\right)\right)=x+C_0$
