討論串[理工] [工數]-高階線性與非線性微分方程
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xy''' + y^2 y''' + 6yy'y'' + 3y'' + 2(y')^3 = 0. (1) + (2) + (3) + (4) + (5) = 0. ∫(1) => ∫ xy''' dx = xy'' - ∫y''dx. ∫[(1) + (4)] => xy'' + 2 ∫y''dx
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令 z = sinx, dz/dx = cosx = sqrt(1-z^2). dy/dx = (dy/dz)(dz/dx) = sqrt(1-z^2) (dy/dz). d^2y/dx = d/dx (sqrt(1-z^2) (dy/dz)). = d/dz (sqrt(1-z^2) (dy/dz
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令x=1/t, => t=1/x, dt/dx=-1/x^2=-t^2. dy/dx = (dy/dt)(dt/dx) = -t^2 (dy/dt). d^2y/dx^2 = d/dx (-t^2 (dy/dt)) = d/dt (-t^2 (dy/dt)) (dt/dx). = (-2t (dy/
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1.Use the change of variable x =1/t to determine the general solution of thedifferential equation.. 4 3 3/x. x y" + 2x y'- y = 8e. -1/x 1/x 3/x. ans:y
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