4y^'-(2/x)y=(-3/2)xy^{5/2}

Lösung

4 y^{^{'}} - (\frac{2}{x}) y = (- \frac{3}{2}) x y^{\frac{5}{2}}

y = \frac{2 3 242 x ^{\frac{1}{2}}}{3 81 x ^{\frac{11}{2}} + 792 c _{1} x ^{\frac{11}{4}} + 1936 c _{1}^{2}}

Schritte zur Lösung

4 y^{'} (x) - (\frac{2}{x}) y = (- \frac{3}{2}) x y^{\frac{5}{2}}

Solve Bernoulli ODE:

y = \frac{2 3 242 x ^{\frac{1}{2}}}{3 81 x ^{\frac{11}{2}} + 792 c _{1} x ^{\frac{11}{4}} + 1936 c _{1}^{2}}

y = \frac{2 3 242 x ^{\frac{1}{2}}}{3 81 x ^{\frac{11}{2}} + 792 c _{1} x ^{\frac{11}{4}} + 1936 c _{1}^{2}}

x \to 0 lim (\frac{sin ( x )}{7 x})

\int \frac{5 x ^{4} + 7 x ^{2} + x + 2}{x ( x ^{2} + 1 ) ^{2}} d x

\int \frac{1}{x ln ( x ^{3} )} d x

\frac{\partial}{\partial x} (e^{x y} cos (y))

\frac{d y}{d x} = \frac{3 y ^{3}}{x ^{2}}, y (3) = 1