Internal problem ID [10250]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1927.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime \prime }\left (t \right )&=a \,{\mathrm e}^{2 x \left (t \right )}-{\mathrm e}^{-x \left (t \right )}+{\mathrm e}^{-2 x \left (t \right )} \left (\cos ^{2}\left (y \left (t \right )\right )\right )\\ y^{\prime \prime }\left (t \right )&={\mathrm e}^{-2 x \left (t \right )} \sin \left (y \left (t \right )\right ) \cos \left (y \left (t \right )\right )-\frac {\sin \left (y \left (t \right )\right )}{\cos \left (y \left (t \right )\right )^{3}} \end {align*}
✗ Solution by Maple
dsolve([diff(x(t),t,t)=a*exp(2*x(t))-exp(-x(t))+exp(-2*x(t))*cos(y(t))^2,diff(y(t),t,t)=exp(-2*x(t))*sin(y(t))*cos(y(t))-sin(y(t))/cos(y(t))^3],singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x''[t]==a*Exp[2*x[t]]-Exp[-x[t]]+Exp[-2*x[t]]*Cos[y[t]]^2,y''[t]==Exp[-2*x[t]]*Sin[y[t]]*Cos[y[t]]-Sin[y[t]]/Cos[y[t]]^3},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Not solved