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6.2 Ordinary Differential Equations • 251θ(t) =100 − 8 t + 2 5 t2 − 175 t3 + 1 13000 t4 −150000 t5 + O(t 6 )When You Cannot Find a Closed Form SolutionIn some instances, you cannot express the solution to a linear ODE inclosed form. In such cases, dsolve may return solutions containing thedata structure DESol. DESol is a place holder representing the solutionof a differential equation without explicitly computing it. Thus, DESolis similar to RootOf, which represents the roots of an expression. Thisallows you to manipulate the resulting expression symbolically prior toattempting another approach.> de := (x^7+x^3-3)*diff(y(x),x,x) + x^4*diff(y(x),x)> + (23*x-17)*y(x);de :=(x 7 + x 3 − 3) ( d2 y(x)) + x 4 ( ddx 2 dxy(x)) + (23 x − 17) y(x)The dsolve command cannot find a closed form solution to de.> dsolve( de, y(x) );y(x) = DESol{( d2(_Y(x)) + x4 ( ddx _Y(x))}(23 x − 17) _Y(x)dx 2 x 7 + x 3 +− 3 x 7 + x 3 ,− 3){_Y(x)}You can now try another method on the DESol itself. For example, finda series approximation.> series(rhs(%), x);