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Bc2

Function: bc2 (<solution>, <xval1>, <yval1>, <xval2>, <yval2>) Solves a boundary value problem for a second order differential equation. Here: <solution> is a general solution to the equation, as found by ode2; <xval1> specifies the value of the independent variable in a first point, in the form <x> = <x1>, and <yval1> gives the value of the dependent variable in that point, in the form <y> = <y1>. The expressions <xval2> and <yval2> give the values for these variables at a second point, using the same form.

F:Dy^2+4*y^2+4*x^2*y+x*cos(x);
x1:-1;
x2:1;
dF:diff(F,Dy);
eqn:diff(F,y)-diff(dF,x)-diff(dF,y)*

See ode2 for an example of its usage.

(%o1)                                true
(%i2) 

Related Examples

bc2-depends-diff-kill

kill(all);

dpends(f[x,y]);

depends(y,x);

Calculate

bc2-cos-diff-euler-integrate-ode2-plot2d-rhs-solve-subst
plot2d([rhs(res), rhs(extr)],[x,-1, 1]);

eqn:(Dy)^2+4*y^2+4*(x...

h:diff(eqn,y);

h1:diff(eqn,Dy);

Calculate

bc2-dependencies-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-dependencies-depends-diff-ode2

Kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-cos-diff-euler-makelist-ode2-plot2d-rhs-solve-subst
plot2d([[discrete, list], rhs(extr)], [x, 0, 1],[xlabel,"x"],[ylabel,"y"]);

eqn:2*(Dy)^2-2*y^2+y*...

h:diff(eqn,y);

h1:diff(eqn,Dy);

Calculate

bc2-diff-ode2-plot2d-rhs
   plot2d(rhs(eqnend),[x,1,3],[xlabel,"x"],[ylabel,"y(x)"]);

eqn:'diff(y,x,2)-y=x*x;

sol:ode2(eqn,y,x);

bc2(sol, x=1, y=1,...

Calculate

bc2-diff-numer-ode2-plot2d-rhs-solve-subst
plot2d([rhs(lab2), rhs(lab3), rhs(lab4)], [x,x1,x2], [xlabel,"x"], [ylabel,"y(x)"], [color, red, green, black], [legend, "y(x)=lab2", "y(x)=lab3", "y(x)=lab4"]);

Psi:2*y1^2-y1*y2+3*y2...

F:2*Dy^2+2*y^2+y*%e^x...

x1:-1;

Calculate