(dx)/(dt)=(2x^2+tsqrt(7t^2+x^2))/(2tx)

解

\frac{d x}{d t} = \frac{2 x ^{2} + t 7 t ^{2} + x ^{2}}{2 t x}

x = \frac{ln ^{2} ( t ) + 4 c _{1} ln ( t ) + 4 c _{1}^{2} - 28 t}{2}, x = - \frac{t ln ^{2} ( t ) + 4 c _{1} ln ( t ) + 4 c _{1}^{2} - 28}{2}

解答ステップ

\frac{d x}{d t} = \frac{2 x ^{2} + t 7 t ^{2} + x ^{2}}{2 t x}

置換を使用して解く:

x = \frac{ln ^{2} ( t ) + 4 c _{1} ln ( t ) + 4 c _{1}^{2} - 28 t}{2}, x = - \frac{t ln ^{2} ( t ) + 4 c _{1} ln ( t ) + 4 c _{1}^{2} - 28}{2}

x = \frac{ln ^{2} ( t ) + 4 c _{1} ln ( t ) + 4 c _{1}^{2} - 28 t}{2}, x = - \frac{t ln ^{2} ( t ) + 4 c _{1} ln ( t ) + 4 c _{1}^{2} - 28}{2}