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1st April 2019, 09:26 #1
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solving differential equations help
I need help in solving differential equations
Code:1 xy'  y = x^2 2 y' y/x = x sinx 3 y' 3x^2 y = (4 x e ^(x^3))/sqrt(1+(x^2)) 4 y'y/x = x cos x

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1st April 2019, 13:32 #2
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Re: solving differential equations help
they are all first order linear ordinary differential equations
there are a variety of methods used, which may be found on the internet
you can check the answers with wolfram alpha:
go to the wolfram alpha website and type something like find y for xy'  y = x^2
enter and wait. it will give you the solution but won't tell you how to do it.

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1st April 2019, 17:26 #3
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Re: solving differential equations help
Hint:
Code:xy'  y = x^2 (y/x)'
Code:y' 3x^2 y = (y e^(x^3))' e^(x^3)
Then
Code:1 x^2 (y/x)' = x^2 > solve (y/x)' = 1 2 x (y/x)' = x sinx > solve (y/x)' = sinx 3 (y e^(x^3))' e^(x^3) = (4 x e ^(x^3))/sqrt(1+(x^2)) > solve (y e^(x^3))' = (4 x)/sqrt(1+(x^2)) 4 x (y/x)' = x cosx > solve (y/x)' = cosx
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