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Differential Equation (exam tomorrow!)

    • Thread Starter

    Hey guys I can't solve this first order DE

    (2e^y - x ) *dy/dx = 1

    Im not sure what method to use and got really confused. Any help appreciated!

    1. Define a new variable v=e^y and rewrite the equation in terms of dv/dx.
    2. Define another new variable u=v/x and rewrite the dv/dx equation in terms du/dx. You should get a separable ODE.
    3. Solve for u(x) then substitute back its value in terms of y and make y the subject of the equation. (May have to use exponentiation and the quadratic equation)
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