First order equations.

The DSOLVE program recognizes and solves the following equation types:

• y'(x)=f(y(x)),
• y'(x)=f(x,y(x)) with f homogenous,
• $y'(x)=g(x)y(x)+h(x)y(x)^\alpha , \quad \alpha \in I\!\!R$ (Bernouilli type)
• y'(x)=f(x)g(y) (separable, if f and g are rational fractions)
• y'(x)=f(x)y(x)+g(x) (linear)

The input is the function f(x,y(x)) or an equation like 'd1Y(X)+Y(X)=2'. Examples:

Y(X)^2+Y(X) DSOLVE (incomplete)
X*Y(X)+1-X^2 DSOLVE (linear)
(Y(X)-X)/(Y(X)+X) DSOLVE (homogenous)
Y(X)^2+X*Y(X) DSOLVE (Bernouilli)

The output may be y as a function of x or x as function of y or x and y as a function of t (parametric solution) for an homogenous ode. The equation type is stored in the ODETYPE variable.