Query 06 Differential Equations

Question:  3.3.4.  If the equation is exact, solve the equation (6 t + y^3 ) y ' + 3 t^2 y = 0, with y(2) = 1.

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Question:  If the equation is exact, solve the equation (6 t + 3 t^3 ) y ' + 6 y + 9/2 t^2 y^2 = -t, with y(2) = 1.  *

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Question:  3.3.6.  If the equation is exact, solve the equation y ' =  - ( y cos(t y) + 1) / (t cos(t y) + 2 y e^y^2) with y(0) = pi.

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Question:  3.3.10.  If N(y, t) * y ' + t^2 + y^2 sin(t) = 0 is exact, what is the most general possible form of N(y, t)?

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Question:  3.3.12.  If y = -t - sqrt( 4 - t^2 ) is the solution of the differential equation (y + a t) y '  + (a y + b t) = 0 with initial condition y(0) = y_0, what are the values of a, b and y_0?

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