# Solving Second Order Differential Equations with NDSolve

I'm trying to solve with the given parameters,

1. X = Y = θ = 0
1. X = Y = 0 and θ = 5°
1. X = Y = 0 and θ = - 5°
1. X = Y = 0 and θ = 15°

Any idea what the protected errors are, I made sure to Clear[functions] beforehand. Will the output always give the input because the output for NDSolve was (5,0,0,0..) and if I used (==) it returned True.

• Check your equations. Some of them may be using the single = (Set) instead of the double == (Equal). Feb 25 at 17:50
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Few problems. You can't have theta''[0]=0 as initial conditions for second order ode. You can't write Cos[theta], it has to be Cos[theta[t]] since theta depends on time. You also used = where it should be ==.

Also DSolve can solve this. Why use numerical if exact can do it?

m = 10;
iner = 1/2;
L = 1/10;
g = 981/100;
f1 = 50;
f2 = 50;
ode1 = (f1 + f2) Cos[theta[t]] - g == m y''[t];
ode2 = -(f1 + f2) Sin[theta[t]] == m x''[t];
ode3 = -(f1 + f2) L == iner *theta''[t];
ic = {theta[0] == 5, theta'[0] == 0, x[0] == 0, x'[0] == 0, y[0] == 0,y'[0] == 0};
sol  = DSolve[ {ode1, ode2, ode3, ic}, {x[t], y[t], theta[t]}, t]


If you want numerical, then

 sol  = NDSolve[ {ode1, ode2, ode3, ic}, {x, y, theta}, {t, 0, 1}]


Plot[Evaluate[{x[t], y[t], theta[t]} /. sol], {t, 0, 1}, PlotRange -> All]