Solve the following: (a) xdx2d2y+dxdy−x1y=lnx (b) y(1−lny)dx2d2y+(1+lny)(dxdy)2=0 (c) dx2d2y+dxdy+(dxdy)3=0

Let's solve these differential equations one by one: (a) x(dx^2)/(dy^2) + (dy)/dx - (1/x)y = lnx To solve this second-order ordinary diff...

Resuelto Solve the following: (a) xdx2d2y+dxdy−x1y=lnx (b)

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Pregunta: Solve the following: (a) xdx2d2y+dxdy−x1y=lnx (b) y(1−lny)dx2d2y+(1+lny)(dxdy)2=0 (c) dx2d2y+dxdy+(dxdy)3=0
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Solución
Paso 1
Let's solve these differential equations one by one:

(a) $x \frac{{d x}^{2}}{{d y}^{2}} + \frac{d y}{d x} - (\frac{1}{x}) y = \ln x$
To solve this second-order ordinary diff...
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Paso 2
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Paso 3
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Respuesta
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Texto de la transcripción de la imagen:

Solve the following: (a)

x \frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - \frac{1}{x} y = ln x

(b)

y (1 - ln y) \frac{d ^{2} y}{d x ^{2}} + (1 + ln y) (\frac{d y}{d x})^{2} = 0

(c)

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + (\frac{d y}{d x})^{3} = 0