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Online Algebra Calculator
Many of users do not use powerful Maxima computer algebra system for systematic work, but for ad hoc algebraic calculations – equations, functions, matrixes, etc. only. To do this job, it is not useful to download the whole application from a web site.
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assume-diff-facts-false-forget-logsimp-ode2
eq: diff(r(t),t,2)-C*...
eq2:diff(r(t), t, 2)=0;
assume(C<0);
assume-cos-display2d-draw-draw2d-explicit-integrate-load-showtime-sin-true
(display2d:false,assu...
x (t) := ''(integrate...
y (t) := ''(integrate...
assume
Run Example
(%i1)assume(A> 0,d> 0,y> 0,%lambda> 0,D> 0); (%o1) [A > 0, d > 0, y > 0, %lambda > 0, D > 0] (%i2) test:4*A^2*cos(%pi*d*y/(%lambda*D))^2; 2 2 %pi d y (%o2) 4 A cos (---------) %lambda D (%i3) l:diff(test,y,1); 2 %pi d y %pi d y 8 %pi d A cos(---------) sin(---------) %lambda D %lambda D (%o3) - ---------------------------------------- %lambda D (%i4) solve(l=0,y); solve: using arc-trig functions to get a solution. Some solutions will be lost. %lambda D (%o4) [y = 0, y = ---------] 2 d (%i5)
Run Example
assume(r> 0); (%o1) [r > 0] (%i2) assume(d> 0); (%o2) [d > 0] (%i3) assume(b> 0); (%o3) [b > 0] (%i4) rr(t):=sqrt(r*r+rp*rp-2*r*rp*cos(t)); (%o4) rr(t) := sqrt(r r + rp rp + (- 2) r rp cos(t)) (%i5) x(t):=rr(t)/(2*d); rr(t) (%o5) x(t) := ----- 2 d (%i6) f(t):=1/d*(6/5-2*x(t)^2+3/2*x(t)^3-5*x(t)^5); 1 6 2 3 3 5 (%o6) f(t) := - (- - 2 x (t) + - x (t) + (- 5) x (t)) d 5 2 (%i7) expand(f(t)*sin(t)); 2 2 5/2 5 (- 2 r rp cos(t) + rp + r ) sin(t) (%o7) - ---------------------------------------- 6 32 d 2 2 3/2 2 3 (- 2 r rp cos(t) + rp + r ) sin(t) r rp cos(t) sin(t) rp sin(t) + ---------------------------------------- + ------------------ - ---------- 4 3 3 16 d d 2 d 2 r sin(t) 6 sin(t) - --------- + -------- 3 5 d 2 d (%i8) integrate(expand(f(t)*sin(t)),t); 2 2 7/2 2 2 5/2 5 (- 2 r rp cos(t) + rp + r ) 3 (- 2 r rp cos(t) + rp + r ) (%o8) - --------------------------------- + --------------------------------- 6 4 224 d r rp 80 d r rp 2 2 2 r rp cos (t) rp cos(t) r cos(t) 6 cos(t) - ------------ + ---------- + --------- - -------- 3 3 3 5 d 2 d 2 d 2 d (%i9) integrate(f(t)*sin(t),t); 2 2 7/2 2 2 5/2 5 (- 2 r rp cos(t) + rp + r ) 3 (- 2 r rp cos(t) + rp + r ) (%o9) (- --------------------------------- + --------------------------------- 5 3 224 d r rp 80 d r rp 2 2 2 - r rp cos (t) + rp cos(t) + r cos(t) 6 cos(t) + --------------------------------------- - --------)/d 2 5 2 d (%i10)
Run Example
assume(x> 0); (%o1) [x > 0] (%i2) f(x):=integrate(1/sqrt(-1+exp(x)*erfc(sqrt(x)) + 2*sqrt(x/%pi)),x); 1 (%o2) f(x) := integrate(----------------------------------------------, x) x sqrt(- 1 + exp(x) erfc(sqrt(x)) + 2 sqrt(---)) %pi (%i3) define(f1(x),diff(f(x),x,1)); 1 (%o3) f1(x) := --------------------------------------- x 2 sqrt(x) sqrt(erfc(sqrt(x)) %e + --------- - 1) sqrt(%pi) (%i4) f1(0.01); 1 (%o4) ---------------------------------- 0.2 sqrt(--------- - 0.10354302003087) sqrt(%pi) (%i5)
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