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受欢迎的代数 >

solvefor y,(dy)/(dx)=x^2+e^x*y^2

解答

求解

y, \frac{d y}{d x} = x^{2} + e^{x} \cdot y^{2}

解答

y = \frac{\frac{d y}{d x} - x ^{2}}{e ^{x}}, y = - \frac{\frac{d y}{d x} - x ^{2}}{e ^{x}}

求解步骤

\frac{d y}{d x} = x^{2} + e^{x} y^{2}

交换两边

x^{2} + e^{x} y^{2} = \frac{d y}{d x}

将

x^{2}

到右边

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

两边除以

e^{x}

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

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

y = \frac{\frac{d y}{d x} - x ^{2}}{e ^{x}}, y = - \frac{\frac{d y}{d x} - x ^{2}}{e ^{x}}

作图

流行的例子

- 2 x^{2} + 7 x - 8 = 0

x^{2} = - 4 x + 21

x^{2} + 1 = - x^{2} + 9

5 x^{2} + 30 x + 40 = 0

-0.5x^2+2000x+6000000=7500000

- 0.5 x^{2} + 2000 x + 6000000 = 7500000