Sr Examen
Ecuación diferencial ((d^3y)/(dx^3))-3((d^2)/(dx^2))-4(dy)/(dx)+12y
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Solución
Ha introducido
[src]
3
d
---(y(x)) d
3 4*--(y(x)) 2
dx dx 3*d 12*y(x)
--------- - ---------- - ---- + ------- = 0
dx dx 3 dx
dx
$$- \frac{3 d^{2}}{dx^{3}} + \frac{12 y{\left(x \right)}}{dx} - \frac{4 \frac{d}{d x} y{\left(x \right)}}{dx} + \frac{\frac{d^{3}}{d x^{3}} y{\left(x \right)}}{dx} = 0$$
-3*d^2/dx^3 + 12*y/dx - 4*y'/dx + y'''/dx = 0
Respuesta
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/ ______________ 2/3 ______________\ / ______________ 2/3 ______________\ / ______________ 3 ___ \
|3 ___ 3 / _____ 8*6 3 ___ 5/6 3 / _____ | |3 ___ 3 / _____ 8*6 3 ___ 5/6 3 / _____ | 3 ___ | 3 / _____ 2*\/ 6 |
x*|\/ 6 *\/ 27 + \/ 681 - -------------------------------- + I*\/ 2 *3 *\/ 27 + \/ 681 | x*|\/ 6 *\/ 27 + \/ 681 - -------------------------------- - I*\/ 2 *3 *\/ 27 + \/ 681 | x*\/ 6 *|- \/ 27 + \/ 681 - -----------------|
| ______________ | | ______________ | | ______________|
| / ___\ 3 / _____ | | / ___\ 3 / _____ | | 3 / _____ |
\ \-1 - I*\/ 3 /*\/ 27 + \/ 681 / \ \-1 + I*\/ 3 /*\/ 27 + \/ 681 / \ \/ 27 + \/ 681 /
----------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------- ------------------------------------------------- 2
6 6 3 d
y(x) = C1*e + C2*e + C3*e + -----
2
4*dx
$$y{\left(x \right)} = C_{1} e^{\frac{x \left(\sqrt[3]{6} \sqrt[3]{\sqrt{681} + 27} - \frac{8 \cdot 6^{\frac{2}{3}}}{\left(-1 - \sqrt{3} i\right) \sqrt[3]{\sqrt{681} + 27}} + \sqrt[3]{2} \cdot 3^{\frac{5}{6}} i \sqrt[3]{\sqrt{681} + 27}\right)}{6}} + C_{2} e^{\frac{x \left(\sqrt[3]{6} \sqrt[3]{\sqrt{681} + 27} - \sqrt[3]{2} \cdot 3^{\frac{5}{6}} i \sqrt[3]{\sqrt{681} + 27} - \frac{8 \cdot 6^{\frac{2}{3}}}{\left(-1 + \sqrt{3} i\right) \sqrt[3]{\sqrt{681} + 27}}\right)}{6}} + C_{3} e^{\frac{\sqrt[3]{6} x \left(- \sqrt[3]{\sqrt{681} + 27} - \frac{2 \sqrt[3]{6}}{\sqrt[3]{\sqrt{681} + 27}}\right)}{3}} + \frac{d^{2}}{4 dx^{2}}$$
Clasificación
nth linear constant coeff undetermined coefficients
nth linear constant coeff variation of parameters
nth linear constant coeff variation of parameters Integral