2x^2y^'=x^2+y^2

Lösung

2 x^{2} y^{^{'}} = x^{2} + y^{2}

y = - \frac{2 x}{ln ( x ) + 2 c _{1}} + \frac{x ln ( x )}{ln ( x ) + 2 c _{1}} + \frac{2 c _{1} x}{ln ( x ) + 2 c _{1}}

Schritte zur Lösung

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

Solve using substitution:

y = - \frac{2 x}{ln ( x ) + 2 c _{1}} + \frac{x ln ( x )}{ln ( x ) + 2 c _{1}} + \frac{2 c _{1} x}{ln ( x ) + 2 c _{1}}

y = - \frac{2 x}{ln ( x ) + 2 c _{1}} + \frac{x ln ( x )}{ln ( x ) + 2 c _{1}} + \frac{2 c _{1} x}{ln ( x ) + 2 c _{1}}

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

5 x (x + 4 y) y^{^{'}} = 5 y (x - 4 y)

3 y^{^{'}} + 7 y = x^{3} - 2 x^{2} + 1

y^{^{'}} = x \cdot y - 3 \cdot x + 3 \cdot y + 3 \cdot y - 9

y^{^{'}} = y + e^{x}, y (0) = (x + c) e^{x}, y (0) = \frac{1}{2}