yy^'+y^'=x,y(2)=2

Lösung

y y^{^{'}} + y^{^{'}} = x, y (2) = 2

y = - 1 + x^{2} + 5

Schritte zur Lösung

y y^{'} (x) + y^{'} (x) = x

Solve separable ODE:

y = - 1 + x^{2} + 5

y = - 1 + x^{2} + 5

\frac{d y}{d t} = t^{2} (1 + y^{2})

\frac{d y}{d x} = \frac{( 2 - x )}{( y - 1 )}

e^{x + 2 y} - e^{- 3 y} y^{^{'}} = 0

4 y^{^{'}} = 1 + x + y + x y

y^{^{'}} + 18 y^{^{'}} + 81 y = 0