2yy^'=x(x^2-16)^{-1/2}

Lösung

2 y y^{^{'}} = x (x^{2} - 16)^{- \frac{1}{2}}

y = \frac{c _{1} ( x ^{2} - 16 ) ^{\frac{1}{2}} + x ^{2} - 16}{( x ^{2} - 16 ) ^{\frac{1}{4}}}, y = - \frac{c _{1} ( x ^{2} - 16 ) ^{\frac{1}{2}} + x ^{2} - 16}{( x ^{2} - 16 ) ^{\frac{1}{4}}}

Schritte zur Lösung

2 y y^{'} (x) = x (x^{2} - 16)^{- \frac{1}{2}}

Solve separable ODE:

y = \frac{c _{1} ( x ^{2} - 16 ) ^{\frac{1}{2}} + x ^{2} - 16}{( x ^{2} - 16 ) ^{\frac{1}{4}}}, y = - \frac{c _{1} ( x ^{2} - 16 ) ^{\frac{1}{2}} + x ^{2} - 16}{( x ^{2} - 16 ) ^{\frac{1}{4}}}

y = \frac{c _{1} ( x ^{2} - 16 ) ^{\frac{1}{2}} + x ^{2} - 16}{( x ^{2} - 16 ) ^{\frac{1}{4}}}, y = - \frac{c _{1} ( x ^{2} - 16 ) ^{\frac{1}{2}} + x ^{2} - 16}{( x ^{2} - 16 ) ^{\frac{1}{4}}}

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

y^{2} y^{^{'}} = x ln (x^{2})

x^{2} y^{^{'}} - y - y^{2} = 0

\frac{d y}{d x} y = x e^{- 6 x} + 6 e^{- x} + x^{7}

\frac{d}{d x} (x^{2} + y^{2}) = \frac{d}{d x} (9)