Ecuaciones Diferenciales Método de Exactas

(a) solve(ode(4*D(y)(x)*y(x) + 3*x, y(x)), Type=ExactFirstOrder,

IgnoreAnalyticConstraints)

(b) solve(ode(D(y)(x) - (x - y(x))/(x + y(x)), y(x)),

Type=ExactFirstOrder, IgnoreAnalyticConstraints)

(c)

solve(ode(2*D(y)(x)*y(x)*x + y(x)^2 - x^2, y(x)),

Type=ExactFirstOrder, IgnoreAnalyticConstraints)

(d) solve(ode(D(y)(x) - x/(x + y(x)), y(x)),Type=ExactFirstOrder,

IgnoreAnalyticConstraints) Warning: Cannot detect the exact first-order ODE.

[ode::exact_first_order]

solve(ode(D(y)(x) - x/(x + y(x)), y(x)),

IgnoreAnalyticConstraints)

(e) solve(ode(D(y)(x) - (x - cos(x)*y(x))/(sin(x) + y(x)), y(x)),

Type=ExactFirstOrder, IgnoreAnalyticConstraints)

(f) solve(ode(D(r)(`θ`) -

(r(`θ`)^2*sin(`θ`))/(2*cos(`θ`)*r(`θ`) -

1), r(`θ`)),Type=ExactFirstOrder, IgnoreAnalyticConstraints)

(g) solve(ode(exp(-x)*y(x) - D(y)(x)*(exp(-x) + 2*y(x)) - sin(x),

y(x)), Type=ExactFirstOrder, IgnoreAnalyticConstraints)

(h) solve(ode(y(x)/x + D(y)(x)*(ln(x) + 2*y(x)) + x^2, y(x)),

Type=ExactFirstOrder, IgnoreAnalyticConstraints)

(i) solve(ode(D(y)(x) + (y(x)*(exp(x) - y(x)))/(exp(x) - 2*x*y(x)),

y(x)), Type=ExactFirstOrder, IgnoreAnalyticConstraints)