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Higher-order ordinary differential equations
Mathematics — Methods · higher-order-odes-nonlinear
Problem Find the form of the solutions of the equation
d y d x d 3 y d x 3 − 2 ( d 2 y d x 2 ) 2 + ( d y d x ) 2 = 0 \frac{dy}{dx}\frac{d^3y}{dx^3} - 2\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = 0 d x d y d x 3 d 3 y − 2 ( d x 2 d 2 y ) 2 + ( d x d y ) 2 = 0 y ( 0 ) = ∞ y(0) = \infty y ( 0 ) = ∞ ∫ z cosech u d u = − ln ( cosech z + coth z ) \int^z \operatorname{cosech} u\, du = -\ln(\operatorname{cosech} z + \coth z) ∫ z cosech u d u = − ln ( cosech z + coth z ) Browse the problem library