OdeSolve | general ODE solver |
OdeTest | test the solution of an ODE |
OdeOrder | return order of an ODE |
OdeSolve(expr1==expr2) |
First and second derivatives are entered as y',y''. Higher order derivatives may be entered as y(n), where n is any integer.
In> OdeSolve( y'' + y == 0 ) Out> C42*Sin(x)+C43*Cos(x); In> OdeSolve( 2*y'' + 3*y' + 5*y == 0 ) Out> Exp(((-3)*x)/4)*(C78*Sin(Sqrt(31/16)*x)+C79*Cos(Sqrt(31/16)*x)); In> OdeSolve( y'' - 4*y == 0 ) Out> C132*Exp((-2)*x)+C136*Exp(2*x); In> OdeSolve( y'' +2*y' + y == 0 ) Out> (C183+C184*x)*Exp(-x); |
OdeTest(eqn,testsol) |
testsol -- test solution
In> OdeTest(y''+y,Sin(x)+Cos(x)) Out> 0; In> OdeTest(y''+2*y,Sin(x)+Cos(x)) Out> Sin(x)+Cos(x); |
OdeOrder(eqn) |
In> OdeOrder(y'' + 2*y' == 0) Out> 2; In> OdeOrder(Sin(x)*y(5) + 2*y' == 0) Out> 5; In> OdeOrder(2*y + Sin(y) == 0) Out> 0; |