2018-11-18 10:34:14 -0600 received badge ● Famous Question (source) 2016-07-24 08:34:00 -0600 received badge ● Notable Question (source) 2015-04-23 07:08:14 -0600 received badge ● Popular Question (source) 2013-04-11 10:25:20 -0600 received badge ● Editor (source) 2013-04-11 10:19:25 -0600 asked a question Solving an ODE system with initial conditions Hi! I want to solve system of equations with initial conditions: $x''(t)=-\gamma x'(t)$ $y''(t)=-g-\gamma y'(t)$ with the initial conditions: $$x(0)=0, y(0)=0, x'(0)=v_0 \cos(\theta), y'(0)=v_0 \sin(\theta).$$ I've solved this with Mathematica with no problem, but I don't know how to work in Sage, and friend has asked me for help. Now, I've searched a bit, and I made this: t, G, g, v0, T = var('t G g v0 T') x(t) = function('x',t) y(t) = function('y',t) assume(g>0) assume(G>0) X = x(t).diff(t,2) == - G*x(t).diff(t,1) Y = y(t).diff(t,2) == - g - G*y(t).diff(t,1) desolve_system([X,Y],[x,y],ics = [0,0,v0*cos(T),v0*sin(T)],ivar=t) And I get, as a result this: [x(t) == -e^(-G*t)*D[0](x)(0)/G + D[0](x)(0)/G, y(t) == -g*t/G - (G*D[0](y)(0) + g)*e^(-G*t)/G^2 + (G^2*v0*cos(T) + G*D[0](y)(0) + g)/G^2] Now, Mathematica will give me entirely different result. So what am I doing wrong? :\ I defined the variables, I defined the functions, made differential equations. I even tried solving the equations separately (without initial conditions), and the solutions are different.