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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.

eqn:(Dy)^2+y^2+4*y*exp(x)-x*sin(x);
h:diff(eqn,y);
 h1:diff(eqn,Dy);
 euler:h-(diff(h1, x) + diff(h1, y)*Dy+diff(h1, Dy)*

See ode2 for an example of its usage.

(%o1)                                true
(%i2) 

Related Examples

bc2-diff-ic2-ode2

eqn:'diff(y,x,2)-y=%e^x;

sol:ode2(eqn,y,x);

ic2(sol,x=-1,y=2,'dif...

Calculate

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

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

dF:diff(F,Dy);

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

Calculate

bc2-diff-ode2

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

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

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

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

x1:-1;

Calculate

bc2-diff-ic2-ode2-ratsimp

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

soln3:ode2(eqn3,y,x);

ratsimp(ic2(soln3,x =...

Calculate

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

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

x1:0;

x2:2;

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-subst
 plot2d(rhs(eqnend),[x,x1,x2],[xlabel,"x"],[ylabel,"y(x)"]);

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

x1:0;

x2:2;

Calculate