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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.

eqn1: diff(y(x),x)=z;
eqn2: diff(z(x),x)=3*z - 2*y + exp^x;
 atvalue(y(x),x=0,2);
 atvalue(z(x),x=0,3);
result:desolve([eqn1,eqn2],[y(x),z(x)]);
  eqn_1:

See ode2 for an example of its usage.

(%o1)                                true
(%i2) 

Related Examples

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

eqn: 'diff(y,x,2)-3*'...

sol: ode2(eqn,y,x);

expr:bc2(sol, x=-1, y...

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(x))^2-4*y(x)^2+...

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

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

Calculate

bc2-cos-diff-numer-ode2-plot2d-rhs-subst
plot2d(rhs(eqnend),[x,x1,x2],[xlabel,"x"],[ylabel,"y(x)"]);

F:Dy^2+4*y^2+4*x^2*y+...

x1:-1;

x2:1;

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-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);

eqnend : bc2(sol, ...

Calculate

bc2-cos-diff-ode2-plot2d-rhs-subst
plot2d(rhs(eqnend),[x,0,2],[xlabel,"x"],[ylabel,"y(x)"]);

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

dF:diff(F,Dy);

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

Calculate

bc2-diff-exp-ode2-plot2d-rhs-sin-solve-subst
plot2d(rhs(total), [x, x1, x2],[xlabel,"x"],[ylabel,"y(x)"]);

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

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

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

Calculate

bc2-diff-ic2-ode2-ratsimp

eqn3:y*('diff(y,x))^3...

soln3:ode2(eqn3,y,x);

ratsimp(ic2(soln3,x=0...

Calculate

bc2-diff-exp-length-makelist-ode2-plot2d-rhs-rk-subst
plot2d ([[discrete, l],rhs(expr)], [x, -1, 1], [xlabel,"x"],[ylabel,"y(x)"],[color, red, green],[legend, "5", "2"]);

/*Необходимо подстави...

/*1.Составляем уравне...

Fdy:diff(F,dy);

Calculate