# How can I solve my second order ODE? [closed]

I am trying to solve

$$\qquad y''(t)=\frac{1}{y(t)^3}-\Big(\frac{y(t)^4+1}{y(t)^5}\Big)y'(t)^2$$

When I try to evaluate

Dsolve[{y''[t] == 1/y[t]^3 - ((y[t]^4 + 1)/y[t]^5)y'[t]^2}, y[t], t]


I just get back

Dsolve[{true}, y[t], t]


How can I fix this?

• This "error" can be produced by inadvertently using the single = sign (Set command) instead of the double == sign (Equal command). To clear the condition either evaluate Remove[y] or quit the kernel and then re-evaluate the DSolve expression. – LouisB Feb 22 at 6:41
• it is DSolve and not Dsolve screen shot !Mathematica graphics – Nasser Feb 22 at 6:57
• If what you got back had True instead of true, then related: (40314), (46214) – Michael E2 Feb 22 at 14:03

See this:

DSolve[{y''[t] == 1/y[t]^3 - ((y[t]^4 + 1)/y[t]^5) y'[t]^2}, y[t], t]

(*  {{y[t] ->
InverseFunction[
Inactive[Integrate][-((Sqrt[2] E^(-(1/(4 K[1]^4))) K[1])/Sqrt[
2 C[1] - ExpIntegralEi[-(1/(2 K[1]^4))]]), {K[1], 1, #1}] &][
t + C[2]]}, {y[t] ->
InverseFunction[
Inactive[Integrate][(Sqrt[2] E^(-(1/(4 K[2]^4))) K[2])/Sqrt[
2 C[1] - ExpIntegralEi[-(1/(2 K[2]^4))]], {K[2], 1, #1}] &][
t + C[2]]}}
*)


Have fun!