Question: solving pdes of the following form

how can i solve pdes of the following form in maple

[tex] tc(t,x)\frac{\partial a(t,x)}{\partial t} - ta(t,x)\frac{\partial c(t,x)}{\partial t} = a(t,x)c(t,x) + t(a(t,x))^2 and be able to find both functions a(t,x) and b(t,x)

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