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    Transcendental DE

    y’’=e^{2y} \; , y(0)=y’(0)=0.
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    Number of solutions of transcendental equation

    Find how many solutions the equation has ? x^2 -2x =(-1)^x \; , x\in \mathbb{Z}.
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    Transcendental equation with several roots

    If someone wants to see how to solve equation x \tan(x) =1 Check this page The way it works is by finding a polynomial with same roots as the transcendental equation.