y^'=(3x)/y sqrt(1+y^2)

Lösung

y^{^{'}} = \frac{3 x}{y} 1 + y^{2}

y = \frac{9 x ^{4} + 12 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}, y = - \frac{9 x ^{4} + 12 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}

Schritte zur Lösung

y^{'} (x) = \frac{3 x}{y} 1 + y^{2}

Solve separable ODE:

y = \frac{9 x ^{4} + 12 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}, y = - \frac{9 x ^{4} + 12 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}

y = \frac{9 x ^{4} + 12 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}, y = - \frac{9 x ^{4} + 12 c _{1} x ^{2} + 4 c _{1}^{2} - 4}{2}

y^{^{'}} = cos^{2} (y), y (0) = 0

+ 2 y d y - ln (t) d t = e^{t} d t

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

\frac{d y}{d x} - \frac{1}{x} y = \frac{1}{x} y^{3}

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