No. Not even for a special case y''(t)+V(t)y(t)=0 for general V(t). Check into any advanced book on differential equations for details, e.g. E. Kamke, Differentialgleichungen: Lösungsmethoden und Lösungen (http://books.google.com/books?id=G7kwO_ADkM0C)

For second order differential equations with dime-dependent variable there is no general solution. And in most of times you can find the analytical solution by application of power series and extracting a recurrence relation between coefficients. However for well-known Bessel equation the solution is a linear combination of two Bessel functions. Check chapters 3 and 5 of Elementary Differential Equations and Boundary Value Problems by Boyce and DiPrima.

The general solution can not be found. Still one can find the solution using classical Peano Baker series if the coefficient matrix of the associated system is a commutative matrix.

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