(e^x-e^-x)sinx/x=f eching

$$\frac { ( e ^ { x } - e ^ { - x } ) \sin x } { x } = f$$

f uchun yechish (complex solution)

$$f=\frac{ie^{\left(2-i\right)x}-ie^{\left(2+i\right)x}-2\sin(x)}{2xe^{x}}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x ga ko'paytirish.

$$\left(e^{x}-e^{-x}\right)\sin(x)=fx$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$fx=\left(e^{x}-e^{-x}\right)\sin(x)$$

e^{x}-e^{-x} ga \sin(x) ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$fx=e^{x}\sin(x)-e^{-x}\sin(x)$$

Tenglama standart shaklda.

$$xf=\sin(x)e^{x}-\frac{\sin(x)}{e^{x}}$$

Ikki tarafini x ga bo‘ling.

$$\frac{xf}{x}=\frac{\sin(x)\left(-\frac{1}{e^{x}}+e^{x}\right)}{x}$$

x ga bo'lish x ga ko'paytirishni bekor qiladi.

$$f=\frac{\sin(x)\left(-\frac{1}{e^{x}}+e^{x}\right)}{x}$$

f uchun yechish

$$f=\frac{\sin(x)\left(e^{2x}-1\right)}{xe^{x}}$$

$$x\neq 0$$

Chiziqli tenglamalarni yechish bo'yicha qadamlar

Tenglamaning ikkala tarafini x ga ko'paytirish.

$$\left(e^{x}-e^{-x}\right)\sin(x)=fx$$

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$fx=\left(e^{x}-e^{-x}\right)\sin(x)$$

e^{x}-e^{-x} ga \sin(x) ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$fx=e^{x}\sin(x)-e^{-x}\sin(x)$$

Tenglama standart shaklda.

$$xf=\sin(x)e^{x}-\frac{\sin(x)}{e^{x}}$$

Ikki tarafini x ga bo‘ling.

$$\frac{xf}{x}=\frac{\sin(x)\left(-\frac{1}{e^{x}}+e^{x}\right)}{x}$$

x ga bo'lish x ga ko'paytirishni bekor qiladi.

$$f=\frac{\sin(x)\left(-\frac{1}{e^{x}}+e^{x}\right)}{x}$$

\sin(x)\left(e^{x}-\frac{1}{e^{x}}\right) ni x ga bo'lish.

$$f=\frac{\sin(x)\left(e^{2x}-1\right)}{xe^{x}}$$