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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: 2*(Dy^2)+2*y(x)^2+3*y(x)*exp(2*x)*sin(x)-5*cos(x);
 fi: y(x0)^2 -4*y(x0) + 3*y(x1)^2;
x_0: -1;
x_1: 1;
/*Дифференцирование оставшейся части. Каждую по своей переменной*/fi_x0: diff(fi, y(x0));
fi_x1: diff(fi, y(x1));
/*Уравнение Эйлера*/Fy: diff(F, y(x));
Fdy: diff(F, Dy);
Fdy1: diff(Fdy,x)+diff(Fdy,y(x))*

See ode2 for an example of its usage.

(%o1)                                true
(%i2) 

Related Examples

bc2-diff-exp-lhs-ode2-plot2d-rhs-solve-subst
plot2d([rhs(res), rhs(sol), lhs(total)], [x, -1, 1], [legend, "4 lab", "3 lab", "2 lab"]);

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

fi: 2*(y(x0)^2) -y(x0...

x_0: -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-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"]);

Psi:y2^2-2*y2;

F:2*Dy^2-2*y^2+y*cos(...

x1:0;

Calculate

bc2-depends-diff-kill-ode2

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

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

F:2*Dy^2+2*y^2+3*y*%e...

dF:diff(F,Dy);

eqn:diff(F,y)-diff(dF...

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"]);

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

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

x1:-1;

Calculate

bc2-diff-first-ode2-plot2d-rhs-second-solve-subst
plot2d([rhs(sol), rhs(total)],[x,-1,1],[xlabel,"x"],[ylabel,"y(x)"]);

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

Fy: diff(F,y(x));

Fdy: diff(F,Dy(x));

Calculate

bc2-depends-diff-kill

kill(all);

depends(f,[x,y]);

depends(y,x);

Calculate

bc2-diff-exp-ode2-plot2d-rhs-solve-subst
plot2d([rhs(res), rhs(sol), rhs(total), rhs(total)], [x, -10, 10], [legend, "4 lab", "3 lab", "2 lab"]);

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

fi: 2*(y(x0)^2) -y(x0...

x_0: -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"]);

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

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

x1:-1;

Calculate