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The Maxima on-line user's manual

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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-diff-integrate-ode2-plot2d-rhs-sin
plot2d(rhs (ps),[x,0,1],[y,0,0.10]);

restart;

ecdif : 'diff(u,x,2)+...

sol2 : ode2(ecdif,u,x);

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, blue], [legend, "y(x)=lab2", "y(x)=lab3", "y(x)=lab4"]);

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

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

x1:-1;

Calculate

bc2-depends-diff-kill

kill(all);

dpends(f[x,y]);

depends(y,x);

Calculate

bc2-cos-diff-exp-ode2-plot2d-rhs-solve-subst
plot2d([rhs(res1), rhs(res2)],[x,-1,1],[xlabel,"x"],[ylabel,"y(x)"]);

('diff(y,x))^2+4*y^2+...

Fy: diff(J,y);

FDy: diff(J,'diff(y,x));

Calculate

bc2-depends-diff-kill

kill(all);

depends(f,[x,y]);

depends(y,x);

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, blue], [legend, "y(x)=lab2", "y(x)=lab3", "y(x)=lab4"]);

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

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

x1:-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, blue], [legend, "y(x)=lab2", "y(x)=lab3", "y(x)=lab4"]);

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

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

x1:-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, blue], [legend, "y(x)=lab2", "y(x)=lab3", "y(x)=lab4"]);

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

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

x1:-1;

Calculate

bc2-cos-diff-ode2-plot2d-rhs
plot2d(rhs(solc),[x,-1,1]);

F:(Dy)^2 + 4*(y)^2 + ...

Fy:diff(F,y);

Fdy:diff(F,Dy);

Calculate