x^3y^'+2x^2y=2cos(3x)y^{-1/2}

Lösung

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

y = \frac{( sin ^{2} ( 3 x ) + 2 c _{1} sin ( 3 x ) + c _{1}^{2} ) ^{\frac{1}{3}}}{x ^{2}}

Schritte zur Lösung

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

Solve Bernoulli ODE:

y = \frac{( sin ^{2} ( 3 x ) + 2 c _{1} sin ( 3 x ) + c _{1}^{2} ) ^{\frac{1}{3}}}{x ^{2}}

y = \frac{( sin ^{2} ( 3 x ) + 2 c _{1} sin ( 3 x ) + c _{1}^{2} ) ^{\frac{1}{3}}}{x ^{2}}

x \to \infty lim (\frac{2 x ^{2} - 9 x - 2}{- 5 x ^{2} - 10 x + 3})

\frac{d}{d x} ((x^{2} + y^{2}))

\frac{\partial}{\partial x} (y^{2} \cdot x^{4} \cdot e^{x} + 2)

\frac{d}{d x} (\frac{e ^{7 x} + e ^{- 7 x}}{x})

\int_{0}^{1} - x^{2} d x