(x+4)(2y+6)dy+xy^2dx=0

Lösung

(x + 4) (2 y + 6) d y + x y^{2} d x = 0

y = \frac{3 x ^{2}}{W ( \frac{3 e ^{\frac{x ^{3} + 12 x ^{2} - 2 c _{1} x ^{2} + 48 x - 16 c _{1} x + 64 - 32 c _{1}}{2 ( x + 4 ) ^{2}}}}{( x + 4 ) ^{2}} ) ( x ^{2} + 8 x + 16 )} + \frac{24 x}{W ( \frac{3 e ^{\frac{x ^{3} + 12 x ^{2} - 2 c _{1} x ^{2} + 48 x - 16 c _{1} x + 64 - 32 c _{1}}{2 ( x + 4 ) ^{2}}}}{( x + 4 ) ^{2}} ) ( x ^{2} + 8 x + 16 )} + \frac{48}{W ( \frac{3 e ^{\frac{x ^{3} + 12 x ^{2} - 2 c _{1} x ^{2} + 48 x - 16 c _{1} x + 64 - 32 c _{1}}{2 ( x + 4 ) ^{2}}}}{( x + 4 ) ^{2}} ) ( x ^{2} + 8 x + 16 )}

Schritte zur Lösung

(x + 4) (2 y + 6) d y + x y^{2} d x = 0

Solve separable ODE:

y = \frac{3 x ^{2}}{W ( \frac{3 e ^{\frac{x ^{3} + 12 x ^{2} - 2 c _{1} x ^{2} + 48 x - 16 c _{1} x + 64 - 32 c _{1}}{2 ( x + 4 ) ^{2}}}}{( x + 4 ) ^{2}} ) ( x ^{2} + 8 x + 16 )} + \frac{24 x}{W ( \frac{3 e ^{\frac{x ^{3} + 12 x ^{2} - 2 c _{1} x ^{2} + 48 x - 16 c _{1} x + 64 - 32 c _{1}}{2 ( x + 4 ) ^{2}}}}{( x + 4 ) ^{2}} ) ( x ^{2} + 8 x + 16 )} + \frac{48}{W ( \frac{3 e ^{\frac{x ^{3} + 12 x ^{2} - 2 c _{1} x ^{2} + 48 x - 16 c _{1} x + 64 - 32 c _{1}}{2 ( x + 4 ) ^{2}}}}{( x + 4 ) ^{2}} ) ( x ^{2} + 8 x + 16 )}

y = \frac{3 x ^{2}}{W ( \frac{3 e ^{\frac{x ^{3} + 12 x ^{2} - 2 c _{1} x ^{2} + 48 x - 16 c _{1} x + 64 - 32 c _{1}}{2 ( x + 4 ) ^{2}}}}{( x + 4 ) ^{2}} ) ( x ^{2} + 8 x + 16 )} + \frac{24 x}{W ( \frac{3 e ^{\frac{x ^{3} + 12 x ^{2} - 2 c _{1} x ^{2} + 48 x - 16 c _{1} x + 64 - 32 c _{1}}{2 ( x + 4 ) ^{2}}}}{( x + 4 ) ^{2}} ) ( x ^{2} + 8 x + 16 )} + \frac{48}{W ( \frac{3 e ^{\frac{x ^{3} + 12 x ^{2} - 2 c _{1} x ^{2} + 48 x - 16 c _{1} x + 64 - 32 c _{1}}{2 ( x + 4 ) ^{2}}}}{( x + 4 ) ^{2}} ) ( x ^{2} + 8 x + 16 )}

\frac{d y}{d x} = 7 x^{2} y

\frac{d y}{d x} = \frac{x}{3 - y}, y (2) = 0

\frac{d y}{d x} = 12 e^{x - y}

x \frac{d y}{d x} + y = 0

x d x + sec (x) sin (y) d y = 0