Find the general solution of the following differential equations
given a known solution y1.
1) x(1-x)y" + 2(1-2x)y' -2y = 0
y1 = 1/x
2) (1-x^2)y"-2xy'+2y = 0 :
y 1 = x.
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Consider the second order Homogeneous equation :
y" + p(x)y' + q(x) = 0
If we know one non-zero solution by any method, then it is easy to find other solution y2(x) which is independent of y1(x).
Thus, y1 and y2 will form basis of solution.
This can be done by taking y = u x where where u(x) is an unknown function.
and solving it for given SOHE.
For Calculation see pic attached to it.
y" + p(x)y' + q(x) = 0
If we know one non-zero solution by any method, then it is easy to find other solution y2(x) which is independent of y1(x).
Thus, y1 and y2 will form basis of solution.
This can be done by taking y = u x where where u(x) is an unknown function.
and solving it for given SOHE.
For Calculation see pic attached to it.
Attachments:
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