(x+y)^2dx+(2xy+x^2-3)dy=0,y(1)=1

Lösung

(x + y)^{2} d x + (2 x y + x^{2} - 3) d y = 0, y (1) = 1

y = \frac{9 - 3 x ^{2} + 81 - 54 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{9 - 3 x ^{2} - 81 - 54 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

Schritte zur Lösung

(x + y)^{2} d x + (2 x y + x^{2} - 3) d y = 0

Solve exact ODE:

y = \frac{9 - 3 x ^{2} + 81 - 54 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{9 - 3 x ^{2} - 81 - 54 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

y = \frac{9 - 3 x ^{2} + 81 - 54 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{9 - 3 x ^{2} - 81 - 54 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

x \to \frac{3}{2} lim (\frac{4 x ^{2} + 12 x + 9}{2 x - 3})

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

\int_{0}^{\infty} x e^{- \frac{x}{2}} d x

\int_{0}^{π} 5 e^{x} sin (x) d x

n = 1 \sum \infty 2