The IVP $$(p^2-25)\frac{d^4s}{dp^4}+p^4\frac{d^3s}{dp^3}+\frac{1}{p^2+1}\frac{ds}{dp}+s=\sin(p)$$ $$s(1)= -1257$$ $$\frac{ds}{dp}\Big\vert_{1} = 16$$ $$\frac{d^2s}{dp^2}\Big\vert_{1} = 10$$ $$\frac{d^3s}{dp^3}\Big\vert_{1} = 6$$ has a unique solution defined on the interval