SharedVariación de Parámetros.sagewsOpen in CoCalc

Resolviendo con SAGE, para comprobar resultados

EDO 1: y10y+25y=x2y''-10y'+25y = x^{2}

### Resolviendp la ED:
x = var("x")
y = function("y")(x)
EDO = diff(y,x,2)-10*diff(y,x)+25*y == x^2
soln = desolve(EDO, y)
show(soln.expand())
K2xe(5x)+125x2+K1e(5x)+4125x+6625\displaystyle K_{2} x e^{\left(5 \, x\right)} + \frac{1}{25} \, x^{2} + K_{1} e^{\left(5 \, x\right)} + \frac{4}{125} \, x + \frac{6}{625}

EDO 2: yy=exy''-y = e^{x}

### Resolviendp la ED:
x = var("x")
y = function("y")(x)
EDO = diff(y,x,2)-y == e^x
soln = desolve(EDO, y)
show(soln.expand())
K2e(x)+K1ex+12xex14ex\displaystyle K_{2} e^{\left(-x\right)} + K_{1} e^{x} + \frac{1}{2} \, x e^{x} - \frac{1}{4} \, e^{x}