(dy)/(dx)=7\sqrt[4]{xy}

Lösung

\frac{d y}{d x} = 7 4 x y

y = \frac{3 3 3 3 614656 x ^{5} + 439040 c _{1} x ^{\frac{15}{4}} + 117600 c _{1}^{2} x ^{\frac{5}{2}} + 14000 c _{1}^{3} x ^{\frac{5}{4}} + 625 c _{1}^{4}}{20 3 20}

Schritte zur Lösung

\frac{d y}{d x} = 7 4 x y

Solve separable ODE:

y = \frac{3 3 3 3 614656 x ^{5} + 439040 c _{1} x ^{\frac{15}{4}} + 117600 c _{1}^{2} x ^{\frac{5}{2}} + 14000 c _{1}^{3} x ^{\frac{5}{4}} + 625 c _{1}^{4}}{20 3 20}

y = \frac{3 3 3 3 614656 x ^{5} + 439040 c _{1} x ^{\frac{15}{4}} + 117600 c _{1}^{2} x ^{\frac{5}{2}} + 14000 c _{1}^{3} x ^{\frac{5}{4}} + 625 c _{1}^{4}}{20 3 20}

\frac{d y}{d t} + [1 + t^{2}] \cdot e^{- t} y = 0, y [0] = 1

\frac{d z}{d t} + e^{2 t + 2 z} = 0

\frac{d y}{d x} = 4 x^{6} y

\frac{d y}{d x} = x y^{2} e^{x}, y (0) = 2

\frac{d y}{d x} = \frac{x ^{2} - 1}{y ^{2}}, y (0) = 2