Find the differential equations with the following general solution?please help me I cannot find the solution I have test on this?

This is the solution of an ordinary DE with constant coefficients. (you should know this)

The auxiliary equation of this DE is formed from the e indices viz : (m+1)(m+3)=0

This expands to m²+4m+3=0

The DE is formed by replacing m by dy/dx, m² by d²y/dx², etc

d²y/dx²+4dy/dx+3y = 0

…………………………..

Another way you can do it is to use differentiation to derive 2 additional equations and then eliminate

the arbitrary constants A,B.

y = Ae⁻˟ + Be⁻³˟ … (i)

dy/dx = −Ae⁻˟ − 3Be⁻³˟ … (ii)

d²y/dx² = Ae⁻˟ + 9Be⁻³˟ … (iii)

(ii)+(iii) ⟹ d²y/dx² + dy/dx = 6Be⁻³˟

(i)+(ii) ⟹ y + dy/dx = −2Be⁻³˟

∴ −3(y+dy/dx) = d²y/dx²+dy/dx ⟹ d²ydx²+4dy/dx+3y = 0

dariel what you mean by that .. can you help me to solve this ?

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