\sqrt[4]{x}dx=(dy)/(\sqrt[4]{y)}

Lösung

4 x d x = \frac{d y}{4 y}

y = \frac{3 3 3 3 256 x ^{5} + 1280 c _{1} x ^{\frac{15}{4}} + 2400 c _{1}^{2} x ^{\frac{5}{2}} + 2000 c _{1}^{3} x ^{\frac{5}{4}} + 625 c _{1}^{4}}{20 3 20}

Schritte zur Lösung

4 x d x = \frac{d y}{4 y}

Solve separable ODE:

y = \frac{3 3 3 3 256 x ^{5} + 1280 c _{1} x ^{\frac{15}{4}} + 2400 c _{1}^{2} x ^{\frac{5}{2}} + 2000 c _{1}^{3} x ^{\frac{5}{4}} + 625 c _{1}^{4}}{20 3 20}

y = \frac{3 3 3 3 256 x ^{5} + 1280 c _{1} x ^{\frac{15}{4}} + 2400 c _{1}^{2} x ^{\frac{5}{2}} + 2000 c _{1}^{3} x ^{\frac{5}{4}} + 625 c _{1}^{4}}{20 3 20}

\frac{d y}{d x} = \frac{y}{x ^{2} - 4}

\frac{d v}{d t} = 9.56 - 0.1 v

y^{^{'}} = \frac{y}{x ^{2} - 4}

d y y^{- 2} = \frac{d x}{- x ^{2} + 144}

y = y^{^{'}} x