### Related

##### desolve-diff

B(x):= %e^x;

eq1: 'diff(x(t), t, 2...

eq2: 'diff(z(t), t, 2...

Calculate

##### desolve-diff

desolve(['diff(f(x),x...

Calculate

##### desolve-diff

desolve(['diff(y(x),x...

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##### desolve-diff

eq1:K*x(t) + 'diff(x(...

eq2:desolve(eq1,x(t));

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? desolve;

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##### desolve-diff

eqn1:'diff(f(x),x)= 2...

eqn2:'diff(g(x),x,2)=...

desolve([eqn1,eqn2]...

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##### desolve-diff

eqn_1:'diff(x,t)=1*x(...

eqn_2:'diff(y,t)=-9*x...

desolve([eqn_1,eqn_2]...

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##### desolve-diff

desolve(diff(y(x),x)+...

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##### desolve-diff-exp

desolve([ diff(x(t),...

diff([ y(t) = C1*exp...

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##### desolve-diff-ev

ed1:'diff(x(t),t)=x(t...

ed2:'diff(y(t),t)=y(t...

[x(t),y(t)]=desolve([...

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### desolve

Run Example
```(%i1)desolve(diff(F(x),x,2)+A*(1.0-exp(B*F(x)))=0,F(x));

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 1.0 by 1/1 = 1.0

rat: replaced 1.0 by 1/1 = 1.0
2                F(x) B
(%o1) F(x) = ilt((F(0) g33270  + (A laplace(%e      , x, g33270)
!
d        !                         3
+ -- (F(x))!     ) g33270 - A)/g33270 , g33270, x)
dx       !
!x = 0
(%i2) ```
Run Example
```eq1:'diff(ta(t),t)=(1/c)*[f(t)-(l+g)*ta(t)+g*tao(t)];
d             g tao(t) - (l + g) ta(t) + f(t)
(%o1)           -- (ta(t)) = [-------------------------------]
dt                           c
(%i2) eq2:'diff(tao(t),t)=(1/co)*(g*ta(t)-g*tao(t));
d             g ta(t) - g tao(t)
(%o2)                  -- (tao(t)) = ------------------
dt                    co
(%i3) desolve([eq1,eq2],[ta(t),tao(t)]);
(%o3) [ta(t) =
g tao(t) - (l + g) ta(t) + f(t)
laplace([-------------------------------], t, g33270) + ta(0)
c
ilt(-------------------------------------------------------------, g33270, t),
g33270
g tao(t) - (l + g) ta(t) + f(t)
tao(t) = ilt((tao(0) co g33270 + g laplace([-------------------------------],
c
2
t, g33270) + ta(0) g)/(co g33270  + g g33270), g33270, t)]
(%i4) ```
Run Example
```gpot: 2;
(%o1)                                  2
(%i2) r: sqrt(x(t)^2 +y(t)^2);
2       2
(%o2)                         sqrt(y (t) + x (t))
(%i3) r_potf: r^-(gpot+1);
1
(%o3)                         ------------------
2       2    3/2
(y (t) + x (t))
(%i4) dgl_xt: 'diff(x(t),t,2)=-x(t)*r_potf;
2
d                     x(t)
(%o4)                  --- (x(t)) = - ------------------
2              2       2    3/2
dt             (y (t) + x (t))
(%i5) dgl_yt: 'diff(y(t),t,2)=-y(t)*r_potf;
2
d                     y(t)
(%o5)                  --- (y(t)) = - ------------------
2              2       2    3/2
dt             (y (t) + x (t))
(%i6) atvalue(x(t),t=0,1);
(%o6)                                  1
(%i7) atvalue(y(t),t=0,0);
(%o7)                                  0
(%i8) atvalue('diff(x(t),t),t=0,0);
(%o8)                                  0
(%i9) atvalue('diff(y(t),t),t=0,1);
(%o9)                                  1
(%i10) desolve([dgl_xt,dgl_yt],[x(t),y(t)]);
x(t)
g33270 - laplace(------------------, t, g33270)
2       2    3/2
(y (t) + x (t))
(%o10) [x(t) = ilt(-----------------------------------------------, g33270,
2
g33270
y(t)
laplace(------------------, t, g33270) - 1
2       2    3/2
(y (t) + x (t))
t), y(t) = ilt(- ------------------------------------------, g33270, t)]
2
g33270
(%i11) ```

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