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Question: Recalcitrant differential equation

Question:Recalcitrant differential equation

Alfred_F 595 Maple 2026
ode dsolve differential-equations
11 hours ago
1

In the attached file, I'd like to solve an ODE as an exercise. Only the "series" option yielded a solution. How can the length of the result series be controlled? Is there a package that leads to a "closed" solution – even using well-known transcendental functions?

restart

ode := (1+f(x))*(diff(f(x), x, x)) = 1+x

(1+f(x))*(diff(diff(f(x), x), x)) = 1+x

 (1)

ics := f(0) = 1, (D(f))(0) = 0

f(0) = 1, (D(f))(0) = 0

 (2)

dsolve({ics, ode}, f(x), series)

f(x) = series(1+(1/4)*x^2+(1/12)*x^3-(1/192)*x^4-(1/240)*x^5+O(x^6),x,6)

 (3)

``

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