Internal problem ID [9508]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1929.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime \prime }\relax (t )&=-\frac {C \left (y \relax (t )\right ) f \left (\sqrt {y^{\prime }\relax (t )^{2}}\right ) x^{\prime }\relax (t )}{\sqrt {x^{\prime }\relax (t )^{2}+y^{\prime }\relax (t )^{2}}}\\ y^{\prime \prime }\relax (t )&=-\frac {C \left (y \relax (t )\right ) f \left (\sqrt {y^{\prime }\relax (t )^{2}}\right ) y^{\prime }\relax (t )}{\sqrt {x^{\prime }\relax (t )^{2}+y^{\prime }\relax (t )^{2}}}-g \end {align*}
✗ Solution by Maple
dsolve({diff(x(t),t,t)=-C(y(t))*f((diff(x(t),x)^2+diff(y(t),t)^2)^(1/2))/(diff(x(t),t)^2+diff(y(t),t)^2)^(1/2)*diff(x(t),t),diff(y(t),t,t)=-C(y(t))*f((diff(x(t),x)^2+diff(y(t),t)^2)^(1/2))/(diff(x(t),t)^2+diff(y(t),t)^2)^(1/2)*diff(y(t),t)-g},{x(t), y(t)}, singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x''[t]==-c[y[t]]*f[(x'[t]^2+y'[t]^2)^(1/2)]/(x'[t]^2+y'[t]^2)^(1/2)*x'[t],y''[t]==-c[y[t]]*f[(x'[t]^2+y'[t]^2)^(1/2)]/(x'[t]^2+y'[t]^2)^(1/2)*y'[t]-g},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Not solved