(a) Find the general solutions of the differential equations x² ² dy + (1+x)y² = 2x³y². dx (b) Show that dy y x = +. dx x y is a homogeneous differential equation. Hence, find the particular satisfies the initial condition (1) = 1

Advanced Engineering Mathematics
10th Edition
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1.
(a) Find the general solutions of the differential equations
dy
dx
-+(1+x)y² = 2x³y².
(b) Show that
dy_y
dx x y
x
is a homogeneous differential equation. Hence, find the particular solution that
satisfies the initial condition y(1) = 1.
Transcribed Image Text:1. (a) Find the general solutions of the differential equations dy dx -+(1+x)y² = 2x³y². (b) Show that dy_y dx x y x is a homogeneous differential equation. Hence, find the particular solution that satisfies the initial condition y(1) = 1.
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