ญ 4. Consider the second ordinary differential equation y" = (2x-5y)y'. (a) Derive the determining equations for the symmetries of equation (2). (b) Solve the determining equations and find the symmetries of (2).
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just need help with part a)
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- Give an example of a differential equation. Identify its type according to linearity, form, order. (Write legibly to avoid confusion, ty:) ) Example: 2y"+y"' = 5 sin xAnswer: Linear Third Order Differential Equations.Let the second order differential equation be: a) Classify the point Xo = 0 b) Determine the two solutions of the differential equation.Consider the differential equation y'= et. (a) Draw its direction field. ? A. y C. 1.1. 10 T (b) Find a general solution to the differential equation help (formulas) (c) Draw a solution on top of the direction field. ? î J.J. į į jį į ]]] J.J.J. TIT i B. D. 111 TT 11111 1 1 1 1 TTT +-+ 1 1 1 1 TT TTT 1 J J J J J 1 T 1 J J T TTT -10| 111 1 T 1 1 1 } } TTT N TTTTTTTT 11 TT TT 1 11 1 ] J -16 JILL IIIII | | | | | TILLI 1 ÿ 1 1 y 1. 1 LI 11 10 1 111 11 LII 111 11111 1. J.J. III]. [|]] |||
- Consider the differential equation y'= 1-y. (a) Find equations for the isoclines corresponding to the slopes 2,1, -1, -2 and 0 in the form y = g(t) (recall, isoclines are curves of the form f(t, y) = C).Determine the constant ? such that the differential equation(??^2? + 2?^2)?? + (?^3+ 4??)?? = 0is exact and solve the resulting exact equation.Q4 (A): Derive the differential equation governing the buckling of the column shown in figure knowing that the column has a uniform circular cross section, then determine the first buckling load? P y L (x,y) TTTT
- y" - 15y + 56y=0 (a) Give the characteristic polynomial for the differential equation. (use r as your variable.) (b) List the roots of the characteristic polynomial for the differential equation. (c) List the basic solutions for the differential equation, i.e. yı(t), y2(t).I) Consider the function: -5.x y = + C,e2* + Cze-5x + C,xe-5x (1) Find a linear homogeneous differential equation of third order with constant coefficients so that the function (1) is a solution of said differential equation.