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Consider the ODE d xy =55x2y2 y wherex >0 dx and let tanh(ax 4) y(x) = where a 6 IR is a constant. X Find the value(s) of a for which y(x) is a solution of the ODE. Hint: Substitute y(x) into the ODE. a = If there is more than one value, then enter them separated by commas, for example -2, 1 If there is no such a, then enter NONE Classify each of the following ODEs as separable, linear, both, or neither. You do not need to solve the ODEs. dy = 2 cosh(x) + 4vy choose dx dy 2(y + 2) choose V = dx X dy = 3 sinh(x) - y tan(x) choose V dxConsider the ODE 1 dy _x5 2 =e 5x , x>0. x2 dx y This ODE can be written as a linear ODE in the form % + P(x)y = Q(x) where 1906) = and (206) = An integrating factor I (x) for this ODE is I = (fully simplify your answer for I (x)). After multiplying by the integrating factor, the ODE becomes d ( ) = dx (substitute in your expression for I (x).) Consider the ODE d dy =251nh(3x)y7 x5y, x>0, y>0. X Using the substitution u = y6 , the ODE can be written as du_ E (give your answer in terms of u and x only)