60.10.15 problem 1927

Internal problem ID [11926]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1927
Date solved : Monday, January 27, 2025 at 11:47:23 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d^{2}}{d t^{2}}x \left (t \right )&=a \,{\mathrm e}^{2 x \left (t \right )}-{\mathrm e}^{-x \left (t \right )}+{\mathrm e}^{-2 x \left (t \right )} \cos \left (y \left (t \right )\right )^{2}\\ \frac {d^{2}}{d t^{2}}y \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: 0.000 (sec). Leaf size: 0

DSolve[{D[x[t],{t,2}]==a*Exp[2*x[t]]-Exp[-x[t]]+Exp[-2*x[t]]*Cos[y[t]]^2,D[y[t],{t,2}]==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