y^'=15\sqrt[4]{xy}

Lösung

y^{^{'}} = 15 4 x y

y = \frac{3 3 3 3 20736 x ^{5} + 6912 c _{1} x ^{\frac{15}{4}} + 864 c _{1}^{2} x ^{\frac{5}{2}} + 48 c _{1}^{3} x ^{\frac{5}{4}} + c _{1}^{4}}{4 3 4}

Schritte zur Lösung

y^{'} (x) = 15 4 x y

Solve separable ODE:

y = \frac{3 3 3 3 20736 x ^{5} + 6912 c _{1} x ^{\frac{15}{4}} + 864 c _{1}^{2} x ^{\frac{5}{2}} + 48 c _{1}^{3} x ^{\frac{5}{4}} + c _{1}^{4}}{4 3 4}

y = \frac{3 3 3 3 20736 x ^{5} + 6912 c _{1} x ^{\frac{15}{4}} + 864 c _{1}^{2} x ^{\frac{5}{2}} + 48 c _{1}^{3} x ^{\frac{5}{4}} + c _{1}^{4}}{4 3 4}

(y^{4} + 1) d x + x y^{3} d y = 0

y^{^{'}} + 6 y tan (2 x) = 0

y^{^{'}} = y ln (x) + y

5 \frac{d x}{d t} + 4 x = 3

- \frac{2 y ^{^{'}}}{y} = k