y^'=(3xe^x)/(ysqrt(5+y^2))

Lösung

y^{^{'}} = \frac{3 x e ^{x}}{y 5 + y ^{2}}

y = 3 54 c_{1} e^{x} x + 81 e^{2 x} x^{2} - 162 e^{2 x} x - 54 c_{1} e^{x} + 81 e^{2 x} + 9 c_{1}^{2} - 5, y = - 3 54 c_{1} e^{x} x + 81 e^{2 x} x^{2} - 162 e^{2 x} x - 54 c_{1} e^{x} + 81 e^{2 x} + 9 c_{1}^{2} - 5

Schritte zur Lösung

y^{'} (x) = \frac{3 x e ^{x}}{y 5 + y ^{2}}

Solve separable ODE:

y = 3 54 c_{1} e^{x} x + 81 e^{2 x} x^{2} - 162 e^{2 x} x - 54 c_{1} e^{x} + 81 e^{2 x} + 9 c_{1}^{2} - 5, y = - 3 54 c_{1} e^{x} x + 81 e^{2 x} x^{2} - 162 e^{2 x} x - 54 c_{1} e^{x} + 81 e^{2 x} + 9 c_{1}^{2} - 5

y = 3 54 c_{1} e^{x} x + 81 e^{2 x} x^{2} - 162 e^{2 x} x - 54 c_{1} e^{x} + 81 e^{2 x} + 9 c_{1}^{2} - 5, y = - 3 54 c_{1} e^{x} x + 81 e^{2 x} x^{2} - 162 e^{2 x} x - 54 c_{1} e^{x} + 81 e^{2 x} + 9 c_{1}^{2} - 5

x ln (x) y^{^{'}} = y - 1

y^{^{'}} = \frac{1 - x ^{2}}{y ^{2}}

y = \frac{x ^{2} ( 2 + x )}{( 1 + x ) ^{2}} y^{^{'}}

[3 x cos (3 x) + sin (3 x) - 3] d x + (2 y + 5) d y = 0

y^{^{'}} = \frac{1 - y ^{2}}{1 - x ^{2}}