The substitution y = xv(x) transforms a homogeneous equation into a separable equation. The latter equation can be solved by direct Y integration, and then replacing u by gives the solution to the original equation. Use this method to solve the differential equation dy dx x² + 3y2² 2xy

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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The substitution y = xv(x) transforms a homogeneous equation into a
separable equation. The latter equation can be solved by direct
integration, and then replacing v by gives the solution to the
Y
x
original equation.
dy
Use this method to solve the differential equation dx
NOTE: Use c for the constant of integration.
y(x)=x√cx-1
x² + 3y²
2xy
Transcribed Image Text:The substitution y = xv(x) transforms a homogeneous equation into a separable equation. The latter equation can be solved by direct integration, and then replacing v by gives the solution to the Y x original equation. dy Use this method to solve the differential equation dx NOTE: Use c for the constant of integration. y(x)=x√cx-1 x² + 3y² 2xy
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