Differential Equation Interval of Solution without Solving: (t^2 - 25)(t^2 - 9)y'' + ty = t

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Find interval of solution without solving the differential equation: cos^2(x)sin(x)y'+ycos^3(x)-1=0

First Order Linear Differential Equations

Interval of Solution without Solving: x*sqrt(x+1)*y''' - y' + xy = 0 , y(1) = y'(1) = 0 , y''(1) = 0