alexaube7289 alexaube7289
  • 09-10-2017
  • Mathematics
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Find the general solution of the given differential equation. x2y' + x(x + 2)y = ex

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LammettHash
LammettHash LammettHash
  • 09-10-2017
[tex]x^2y'+x(x+2)y=e^x[/tex]
[tex]x^2e^xy'+x(x+2)e^xy=e^{2x}[/tex]
[tex]\bigg(x^2e^xy\bigg)'=e^{2x}[/tex]
[tex]x^2e^xy=\dfrac{e^{2x}}2+C[/tex]
[tex]y=\dfrac{e^x}{2x^2}+\dfrac C{x^2e^x}[/tex]
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