sqrt(x)(dy)/(dx)=e^{7y+sqrt(x)},x>0

Lösung

x \frac{d y}{d x} = e^{7 y + x}, x > 0

y = - \frac{ln ( - 14 e ^{x} - c _{1} )}{7}

Schritte zur Lösung

x \frac{d y}{d x} = e^{7 y + x}

Solve separable ODE:

y = - \frac{ln ( - 14 e ^{x} - c _{1} )}{7}

y = - \frac{ln ( - 14 e ^{x} - c _{1} )}{7}

x y^{^{'}} = 1 - y

(\frac{d ^{2} x}{d x ^{2}} + 4 \frac{d y}{d x} + 20 y)^{2} = 0

\frac{d p}{d t} = 5 p - p^{2}

y^{^{'}} + 3 x y = 0

y^{^{'}} = - y + 2