(dy)/(dx)=(1+4x)(sqrt(y))

Lösung

\frac{d y}{d x} = (1 + 4 x) (y)

y = \frac{x ^{2}}{4} + \frac{c _{1} x}{2} + \frac{c _{1}^{2}}{4} + x^{3} + c_{1} x^{2} + x^{4}

Schritte zur Lösung

\frac{d y}{d x} = (1 + 4 x) (y)

Solve separable ODE:

y = \frac{x ^{2}}{4} + \frac{c _{1} x}{2} + \frac{c _{1}^{2}}{4} + x^{3} + c_{1} x^{2} + x^{4}

y = \frac{x ^{2}}{4} + \frac{c _{1} x}{2} + \frac{c _{1}^{2}}{4} + x^{3} + c_{1} x^{2} + x^{4}

e^{x + y} d y - d x = 0

\frac{1}{y} \cdot \frac{d y}{d x} = 10

\frac{d x}{d y} = 0.2 x y

y^{^{'}} + \frac{3}{2} y = \frac{3}{2}

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