solvefor y,f=-(40000x)/((3+x^2+2y^2)^2)

Lösung

löse nach

y, f = - \frac{40000 x}{( 3 + x ^{2} + 2 y ^{2} ) ^{2}}

y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}; f \neq = 0

Schritte zur Lösung

f = - \frac{40000 x}{( 3 + x ^{2} + 2 y ^{2} ) ^{2}}

Multipliziere beide Seiten mit

(3 + x^{2} + 2 y^{2})^{2}

f (3 + x^{2} + 2 y^{2})^{2} = - 40000 x

Löse

f (3 + x^{2} + 2 y^{2})^{2} = - 40000 x : y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}; f \neq = 0

y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( - \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} )}{2}, y = \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} cos \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2} + i \frac{f 40000 x + 9 f + x ^{4} f + 6 x ^{2} f}{2 f} sin \frac{arctan ( \frac{200 x f}{f ( 3 + x ^{2} )} ) + 2 π}{2}; f \neq = 0