solve ivp y''+4y=2x ,y(0)=1,y'(0)=2
For the complimentary solution (i.e. solving y''+4y = 0) which you'll need you can follow the basic process outlined at http://tutorial.math.lamar.edu/Classes/DE/ComplexRoots.aspx Then for the particular solution you can use either Undetermined Coefficients (probably easiest for this problem) at, http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx Or variation of parameters at http://tutorial.math.lamar.edu/Classes/DE/VariationofParameters.aspx. The first and second example on the Undetermined Coefficients page shows how to solve a full IVP using this process.
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