Question: how to dsolve this system

there is a triangle, one side is t, another side is sqrt(1-t^2), however this do not need sqrt

i use sin law, can not dsolved the following equation, it can onlyl be solved for right angled triangle

is it only in circle's triangle be solved? 

besides triangle, the goal of mine to use another shape 

ode := diff(u(t),t)-f(t)=0,diff(f(t),t)+t*f(t)=0,diff(f(t),t$2)+(t*sin(a)*sin(b))^2*f(t)=0;  

ode := diff(u(t),t)-f(t)=0,diff(f(t),t)+t*f(t)=0,diff(f(t),t$2)+(t*sin(60)*sin(40))^2*f(t)=0;  


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