Question

Solve Legendre’s equation for the given initial conditions. (1 - x2)y - 2xy + 6y = 0

Answer 1

MuPAD can be used to solve both symbolic and numeric types of calculations. MuPAD can be run by entering mupadwelcome in the command window.

 

To solve a differential equation and get the result in explicit series, the solve function can be used.

To calculate the Legendre\'s equation, enter the following lines in MuPAD:

 

Define the differential equation:

eqn:=ode({(1-x^2)*y\'\'(x)-2*x*y\'(x)+6*y(x)=0,y(0)=5, y\'(0)=0}, y(x));

 

Solve the differential equation:

solve(eqn)

 

The result obtained is:

Define the differential equation:

Solve the differential equation:

 

MuPAD can be used to solve both symbolic and numeric types of calculations. MuPAD can be run by entering mupadwelcome in the command window.

To solve a differential equation and get the result in explicit series, the solve function can be used.

 

To calculate the Legendre\'s equation, enter the following lines in MuPAD:

 

Define the differential equation:

eqn:=ode({(1-x^2)*y\'\'(x)-2*x*y\'(x)+6*y(x)=0,y(0)=5, y\'(0)=0}, y(x));

Solve the differential equation:

solve(eqn)

The result obtained is:

 

Define the differential equation:

Solve the differential equation:

solve(eqn)

{5 - 15x2}

 

Thus, the series solution of the given Legendre\'s equation has been calculated.

Thus, the series solution of the given Legendre\'s equation has been calculated.