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}}

\int \frac{sin ( x )}{1 - 2 cos ( x )} d x

\int e^{x} cos (9 x) d x

\frac{\partial}{\partial x} (5 x^{4} + y^{8})

\frac{d}{d x} ((\frac{3 x + 512}{x + 1})^{\frac{2}{3}})

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