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受欢迎的代数 >

solvefor x,(19)y=(c_{1}+c_{2}x)*e^x

解答

求解

x, (19) \cdot y = (c_{1} + c_{2} \cdot x) \cdot e^{x}

解答

x = W (\frac{19 y e ^{\frac{c _{1}}{c _{2}}}}{c _{2}}) - \frac{c _{1}}{c _{2}}

求解步骤

(19) y = (c_{1} + c_{2} x) e^{x}

用

x + \frac{c _{1}}{c _{2}} = u

和

x = u - \frac{c _{1}}{c _{2}}

改写方程式

19 y = (c_{1} + c_{2} (u - \frac{c _{1}}{c _{2}})) e^{u - \frac{c _{1}}{c _{2}}}

化简

19 y = e^{u - \frac{c _{1}}{c _{2}}} c_{2} u

改写

19 y = e^{u - \frac{c _{1}}{c _{2}}} c_{2} u

为朗伯形式:

e^{u} u = \frac{19 y e ^{\frac{c _{1}}{c _{2}}}}{c _{2}}

解

e^{u} u = \frac{19 y e ^{\frac{c _{1}}{c _{2}}}}{c _{2}} : u = W (\frac{19 y e ^{\frac{c _{1}}{c _{2}}}}{c _{2}})

u = W (\frac{19 y e ^{\frac{c _{1}}{c _{2}}}}{c _{2}})

代回

u = x + \frac{c _{1}}{c _{2}}

，求解

x

解

x + \frac{c _{1}}{c _{2}} = W (\frac{19 y e ^{\frac{c _{1}}{c _{2}}}}{c _{2}}) : x = W (\frac{19 y e ^{\frac{c _{1}}{c _{2}}}}{c _{2}}) - \frac{c _{1}}{c _{2}}

x = W (\frac{19 y e ^{\frac{c _{1}}{c _{2}}}}{c _{2}}) - \frac{c _{1}}{c _{2}}

作图

流行的例子

(sqrt(5+\sqrt{24)})^x+(sqrt(5-\sqrt{24)})^x=10

(5 + 24)^{x} + (5 - 24)^{x} = 10

7^{1-x}=49^{3x+1}

7^{1 - x} = 4 9^{3 x + 1}

solvefor x,e^y=2^x

so l v e f or x, e^{y} = 2^{x}

2^{2x}-2^{x+1}=8

2^{2 x} - 2^{x + 1} = 8

9^{x} = 3^{x} - 3