(2x+1)((dy)/(dx))+y=(2x+1)^{3/2}

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

y^{^{''}} + 3 y = - 48 x^{2} e^{3 x}

f (x) = arcsinh (x)

\int - 510 x^{2} + 3414 x + 1998 d x

d er i v a t i v e f (x) = (9 - x^{3})^{- 2}

10 y^{^{''}} + 2 y^{^{'}} + 5 y = 0