> I don't know how to do the equality
> Please help me.
To say the least, the question is not too clear. Maybe that's what you
are looking for?
(%i4) ? ode2;
-- Function: ode2 (<eqn>, <dvar>, <ivar>)
The function `ode2' solves an ordinary differential equation (ODE)
of first or second order. It takes three arguments: an ODE given by
<eqn>, the dependent variable <dvar>, and the independent variable
<ivar>. When successful, it returns either an explicit or implicit
solution for the dependent variable. `%c' is used to represent the
integration constant in the case of first-order equations, and
`%k1' and `%k2' the constants for second-order equations. The
dependence of the dependent variable on the independent variable
does not have to be written explicitly, as in the case of
`desolve', but the independent variable must always be given as the
third argument.
If `ode2' cannot obtain a solution for whatever reason, it returns
`false', after perhaps printing out an error message. The methods
implemented for first order equations in the order in which they
are tested are: linear, separable, exact - perhaps requiring an
integrating factor, homogeneous, Bernoulli's equation, and a
generalized homogeneous method. The types of second-order
equations which can be solved are: constant coefficients, exact,
linear homogeneous with non-constant coefficients which can be
transformed to constant coefficients, the Euler or
equi-dimensional equation, equations solvable by the method of
variation of parameters, and equations which are free of either the
independent or of the dependent variable so that they can be
reduced to two first order linear equations to be solved
sequentially.
In the course of solving ODE's, several variables are set purely
for informational purposes: `method' denotes the method of solution
used (e.g., `linear'), `intfactor' denotes any integrating factor
used, `odeindex' denotes the index for Bernoulli's method or for
the generalized homogeneous method, and `yp' denotes the
particular solution for the variation of parameters technique.
In order to solve initial value problems (IVP) functions `ic1' and
`ic2' are available for first and second order equations, and to
solve second-order boundary value problems (BVP) the function `bc2'
can be used.
Example:
(%i1) x^2*'diff(y,x) + 3*y*x = sin(x)/x;
2 dy sin(x)
(%o1) x -- + 3 x y = ------
dx x
(%i2) ode2(%,y,x);
%c - cos(x)
(%o2) y = -----------
3
x
(%i3) ic1(%o2,x=%pi,y=0);
cos(x) + 1
(%o3) y = - ----------
3
x
(%i4) 'diff(y,x,2) + y*'diff(y,x)^3 = 0;
2
d y dy 3
(%o4) --- + y (--) = 0
2 dx
dx
(%i5) ode2(%,y,x);
3
y + 6 %k1 y
(%o5) ------------ = x + %k2
6
(%i6) ratsimp(ic2(%o5,x=0,y=0,'diff(y,x)=2));
3
2 y - 3 y
(%o6) - ---------- = x
6
(%i7) bc2(%o5,x=0,y=1,x=1,y=3);
3
y - 10 y 3
(%o7) --------- = x - -
6 2
(%o4) true