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Differential Equations

fricas
y := operator y
 (1)
Type: BasicOperator?
fricas
deq := D(y(x),x)=(1+y(x)^2)/(1+2*x*y(x))
 (2)
Type: Equation(Expression(Integer))
fricas
solve(deq,y,x)
 (3)
Type: Union(Expression(Integer),...)
fricas
deq := D(y(x),x,3)+D(y(x),x,2)+D(y(x),x,1)+y(x)=x*sin(x)
 (4)
Type: Equation(Expression(Integer))
fricas
solve(deq,y,x)
 (5)
Type: Union(Record(particular: Expression(Integer),basis: List(Expression(Integer))),...)

test solution

fricas
deq := D(y(x),x)=(a+y(x)^2)/(b+2*x^2*y(2*x))
 (6)
Type: Equation(Expression(Integer))
fricas
solve(deq,y,x)
>> Error detected within library code:
getfreelincoeff: not a linear ordinary differential equation

Linear non homog equation

fricas
deq := D(y(x),x) = y(x)^2 + 2 * y(x) + 1
 (7)
Type: Equation(Expression(Integer))
fricas
solve(deq,y,x)
 (8)
Type: Union(Expression(Integer),...)
fricas
z := operator z
 (9)
Type: BasicOperator?
fricas
deq2 := D(z(x),x) = exp(y(x))/(1 - d * y(x))
 (10)
Type: Equation(Expression(Integer))
fricas
solve(deq2,z,x)
 (11)
Type: Union(Record(particular: Expression(Integer),basis: List(Expression(Integer))),...)

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